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Questions and Answers
In the linear equation ax + b = 0, after moving the constant term to the right side, the equation becomes $ax = ______$
In the linear equation ax + b = 0, after moving the constant term to the right side, the equation becomes $ax = ______$
-b
After dividing both sides of the equation ax = -b by 'a', the equation becomes $x = ______$
After dividing both sides of the equation ax = -b by 'a', the equation becomes $x = ______$
-b / a
In the equation 3x + 5 = 0, after moving the constant term to the right side, the equation becomes $3x = ______$
In the equation 3x + 5 = 0, after moving the constant term to the right side, the equation becomes $3x = ______$
-5
After dividing both sides of the equation 3x = -5 by 3, the equation becomes $x = ______$
After dividing both sides of the equation 3x = -5 by 3, the equation becomes $x = ______$
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In the equation ax + bx = cx + d, after combining like terms, the equation becomes $(a + b)x = ______$
In the equation ax + bx = cx + d, after combining like terms, the equation becomes $(a + b)x = ______$
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If the given linear equation has multiples of 'x' on both sides, that is, ax + bx = cx + d, you can proceed by replacing ax + bx = cx + d with $(a + b)x = ______$
If the given linear equation has multiples of 'x' on both sides, that is, ax + bx = cx + d, you can proceed by replacing ax + bx = cx + d with $(a + b)x = ______$
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Step 2: Move the constant term (______) to the right side of the equation. Replace (a + b)x = ______ with (a + b)x = -\left(______\right).
Step 2: Move the constant term (______) to the right side of the equation. Replace (a + b)x = ______ with (a + b)x = -\left(______\right).
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Step 3: Divide both sides of the equation by ______. Replace ______x = -\left(c + d\right) with x = -\frac{\left(c + d\right)}{\left(a + b\right)}.
Step 3: Divide both sides of the equation by ______. Replace ______x = -\left(c + d\right) with x = -\frac{\left(c + d\right)}{\left(a + b\right)}.
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Step 4: Answer the question "What is the value of x." Substitute the value of ______ and -(c + d) into the expression for x. For example, consider the equation 2x^2 + 3x = 5x - 4. 1. Combine like terms: 2x^2 + 3x = 5x - 4 becomes x^2 + 3x = 5x - 4.
Step 4: Answer the question "What is the value of x." Substitute the value of ______ and -(c + d) into the expression for x. For example, consider the equation 2x^2 + 3x = 5x - 4. 1. Combine like terms: 2x^2 + 3x = 5x - 4 becomes x^2 + 3x = 5x - 4.
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Step 2: Move the constant term (______) to the right side of the equation. Replace ax^2 + bx = cx^2 + d with ax^2 + bx = -\left(______\right).
Step 2: Move the constant term (______) to the right side of the equation. Replace ax^2 + bx = cx^2 + d with ax^2 + bx = -\left(______\right).
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Step 3: Divide both sides of the equation by ______. Replace ax^2 + bx = -\left(c + d\right) with x^2 = -\frac{\left(c + d\right)}{\left(a + b\right)}.
Step 3: Divide both sides of the equation by ______. Replace ax^2 + bx = -\left(c + d\right) with x^2 = -\frac{\left(c + d\right)}{\left(a + b\right)}.
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Step 4: Answer the question "What is the value of x^2." Substitute the value of ______ and -(c + d) into the expression for x^2. For example, consider the equation 2x^2 + 3x = 5x^2 - 4. 1. Combine like terms: 2x^2 + 3x = 5x^2 - 4 becomes 3x^2 = 2x - 4.
Step 4: Answer the question "What is the value of x^2." Substitute the value of ______ and -(c + d) into the expression for x^2. For example, consider the equation 2x^2 + 3x = 5x^2 - 4. 1. Combine like terms: 2x^2 + 3x = 5x^2 - 4 becomes 3x^2 = 2x - 4.
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Step 2: Move the constant term (______) to the right side of the equation.
Step 2: Move the constant term (______) to the right side of the equation.
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Step 1: Combine like terms. Replace ______ = cx^3 + d with (a + b)x^2 = c + d.
Step 1: Combine like terms. Replace ______ = cx^3 + d with (a + b)x^2 = c + d.
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Step 2: Move the constant term (______) to the right side of the equation.
Step 2: Move the constant term (______) to the right side of the equation.
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What is the value of x^2? Substitute the value of ______ and -(c + d) into the expression for x^2.
What is the value of x^2? Substitute the value of ______ and -(c + d) into the expression for x^2.
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Study Notes
Solving Linear Equations
Linear equations play a fundamental role in mathematics as they are used to represent relationships between two variables. These equations can be written in the form ax + b = 0, where a and b are constants, and x is the variable. In this section, we will discuss how to solve linear equations for x.
The Basic Process for Solving Linear Equations
-
Step 1: Move the constant term (
b) to the right side of the equation.Replace the original equation
ax + b = 0withax = -b. -
Step 2: Divide both sides of the equation by
a.Replace
ax = -bwithx = -b / a. -
Step 3: Answer the question "What is the value of
x?"Substitute the value of
aandbfrom the original equation into the expression forx.
For example, consider the equation 3x + 5 = 0.
- Move the constant term (
5) to the right side of the equation:3x = -5. - Divide both sides by
3:x = -5 / 3. - Substitute the values of
aandbinto the expression forx:x = -5 / 3.
The value of x is -5 / 3.
Solving Linear Equations with Multiples of x on Both Sides
If the given linear equation has multiples of x on both sides, that is, ax + bx = cx + d, you can proceed as follows:
-
Step 1: Combine like terms.
Replace
ax + bx = cx + dwith(a + b)x = c + d. -
Step 2: Move the constant term (
c + d) to the right side of the equation.Replace
(a + b)x = c + dwith(a + b)x = -(c + d). -
Step 3: Divide both sides of the equation by
(a + b).Replace
(a + b)x = -(c + d)withx = -(c + d) / (a + b). -
Step 4: Answer the question "What is the value of
x?"Substitute the value of
(a + b)and-(c + d)into the expression forx.
For example, consider the equation 2x^2 + 3x = 5x - 4.
- Combine like terms:
2x^2 + 3x = 5x - 4becomesx^2 + 3x = 5x - 4. - Move the constant term (
5x - 4) to the right side of the equation:x^2 + 3x = -(5x - 4). - Divide both sides by
(1 + 3):x = -(5x - 4) / (1 + 3) = -(5x - 4) / 4. - Substitute the values of
(1 + 3)and-(5x - 4)into the expression forx:x = -(5x - 4) / 4.
The value of x is -(5x - 4) / 4.
Solving Linear Equations with Multiples of x^2 on Both Sides
If the given linear equation has multiples of x^2 on both sides, that is, ax^2 + bx = cx^2 + d, you can proceed as follows:
-
Step 1: Combine like terms.
Replace
ax^2 + bx = cx^2 + dwith(a + b)x^2 = c + d. -
Step 2: Move the constant term (
c + d) to the right side of the equation.Replace
(a + b)x^2 = c + dwith(a + b)x^2 = -(c + d). -
Step 3: Divide both sides of the equation by
(a + b).Replace
(a + b)x^2 = -(c + d)withx^2 = -(c + d) / (a + b). -
Step 4: Answer the question "What is the value of
x^2?"Substitute the value of
(a + b)and-(c + d)into the expression forx^2.
For example, consider the equation 2x^2 + 3x = 5x^2 - 4.
- Combine like terms:
2x^2 + 3x = 5x^2 - 4becomes3x^2 = 2x - 4. - Move the constant term (
2x - 4) to the right side of the equation:3x^2 = -(2x - 4). - Divide both sides by
3:x^2 = -(2x - 4) / 3. - Substitute the values of
3and-(2x - 4)into the expression forx^2:x^2 = -(2x - 4) / 3.
The value of x^2 is -(2x - 4) / 3.
Solving Linear Equations with Multiples of x^3 on Both Sides
If the given linear equation has multiples of x^3 on both sides, that is, ax^3 + bx^2 = cx^3 + d, you can proceed as follows:
-
Step 1: Combine like terms.
Replace
ax^3 + bx^2 = cx^3 + dwith(a + b)x^2 = c + d. -
Step 2: Move the constant term (
c + d) to the right side of the equation.
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Description
Learn about the basic process for solving linear equations and how to handle equations with multiples of x, x^2, or x^3 on both sides. Practice solving linear equations step by step with examples.
