Solving Linear Equations: Addition and Subtraction Properties of Equality

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What is the result of $0.2 \times 100$ according to the information provided?

0.25

20

25 (correct)

5

What operation is primarily used in 'LINEAR EQUATIONS PRACTICE' as mentioned in the text?

Addition (correct)

Multiplication

Division

Subtraction

What is the result of $0.05 + 0.25$ based on the information provided?

0.2 (correct)

25

1

20

Which of the following is a false statement according to the text?

$9 = 4$ Signup and view all the answers

What is the implied calculation for the expression '27' in the provided text?

$3^3$ Signup and view all the answers

What is the goal of solving a linear equation?

To find the value of the variable that makes the equation true Signup and view all the answers

Which property of equality involves adding the same value to both sides of an equation?

Addition property of equality Signup and view all the answers

If 2x + 5 = 15, what should be done first to isolate x?

Subtract 5 from both sides Signup and view all the answers

What should be multiplied on both sides to clear fractions in an equation?

The least common denominator (LCD) Signup and view all the answers

Which step comes first when solving a linear equation in one variable?

Simplify both sides of the equation Signup and view all the answers

When is it necessary to clear decimals in an equation?

When the decimals are not integral Signup and view all the answers

What is the value of $5(7 + 3)$?

25 Signup and view all the answers

If $2x - 3 = 7$, what is the value of $x$?

10 Signup and view all the answers

What type of equation is revealed when solving for a variable and it results in a false statement, such as $7 = 3$?

Contradiction Signup and view all the answers

Which of the following is equivalent to $3(4 + 2) - 5$?

$14 - 5$ Signup and view all the answers

When solving an equation and the variables are eliminated to reveal a true statement, like $13 = 13$, what is this type of equation called?

Identity Signup and view all the answers

Solve for $y$ in the equation $2y + 8 = 16$.

$y = 4$ Signup and view all the answers

In the context of solving equations, what does it mean when a solution checks out?

The solution has been substituted back into the original equation successfully Signup and view all the answers

What is the solution to the equation $4(x - 3) = 8$?

$x = 2$ Signup and view all the answers

What should you do after using multiplication or division properties of equality to solve an equation?

Substitute your solution into the original equation Signup and view all the answers

If $3y - 5 = 7$, what is the value of $y$?

$y = 4$ Signup and view all the answers

If you multiply an equation by its reciprocal, what type of operation are you performing?

Division Signup and view all the answers

What is the outcome when solving an equation and it leads to a situation where all real numbers are solutions?

All real numbers Signup and view all the answers

What is the solution to the equation $15x - 6 = 9$?

$x = -\frac{3}{5}$ Signup and view all the answers

What is the solution set of $3(2x - 1) = 5$?

$x = \frac{4}{3}$ Signup and view all the answers

What does the equation $6(x + 2) = 4(3 - x)$ simplify to?

$x = -2$ Signup and view all the answers

Which of the following equations has no solution?

$6(x - 4) + 7 = 8(x + 1)$ Signup and view all the answers

What is the value of $x$ in the equation $\frac{x}{2} - 3 = \frac{3x + 9}{4}$?

$x = -24$ Signup and view all the answers