Worksheet on linear equations in one variable includes various problems and conceptual questions.
Understand the Problem
The question is primarily dealing with linear equations, asking for solutions to specific problems, theoretical concepts, and true/false statements related to this algebraic topic.
Answer
None of the Q1 equations have solutions that are neither fractions nor integers. For Q2, $x = -\frac{b}{a}$; for Q6, $x = \frac{4}{5}$; for Q10, $x = 4$.
Answer for screen readers
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The equation solutions for Q1 show:
- (a) $x = 0$, an integer
- (b) $x = 5$, an integer
- (c) $x = 6$, an integer
- (d) $x = 2$, an integer
Answer: None are fractions or non-integers.
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For Q2, $x = -\frac{b}{a}$.
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For Q6, $x = \frac{4}{5}$.
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For Q10, $x = 4$.
Steps to Solve
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Identify the equation types Review the equations provided and categorize them based on their structure, such as linear or not. For example, equations of form $ax + b = c$ are linear.
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Evaluate each equation in Q1 Assess the equations:
- $3x + 2 = 5x + 2$
- $4x - 18 = 2$
- $4x + 7 = 7 + 2$
- $5x = 8 - 4$
Solve for $x$ in each equation to determine if the solution is an integer, fraction, or neither.
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Solve the equation from Q2 The equation is $ax + b = 0$. To solve for $x$, rearrange: $$ ax = -b $$ Then isolate $x$: $$ x = -\frac{b}{a} $$
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Solve the equation from Q6 For $3x - 4 = -2x$, first bring like terms together: $$ 3x + 2x = 4 $$ Then simplify: $$ 5x = 4 $$ Finally, isolate $x$: $$ x = \frac{4}{5} $$
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Evaluate Q10 The equation is $3x - 3 = 9$. Transpose $-3$ to the right: $$ 3x = 9 + 3 $$ Solve for $x$: $$ 3x = 12 $$ Finally, isolate $x$: $$ x = 4 $$
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The equation solutions for Q1 show:
- (a) $x = 0$, an integer
- (b) $x = 5$, an integer
- (c) $x = 6$, an integer
- (d) $x = 2$, an integer
Answer: None are fractions or non-integers.
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For Q2, $x = -\frac{b}{a}$.
-
For Q6, $x = \frac{4}{5}$.
-
For Q10, $x = 4$.
More Information
These equations and their solutions illustrate basic principles of solving linear equations in one variable. Understanding how to manipulate equations and isolate variables is fundamental in algebra.
Tips
- Confusing the signs during transposition.
- Not fully isolating the variable before solving.
- Overlooking the need to check if a solution is a fraction or an integer.
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