Solving Equations Unit Review

Solve:

• -8

• 1

• -8

• 36

Translate the problem: Two times a number plus ten equals twenty.

• 2x + 10 = 20

• 20 = 2x

• 2(100)= 20

Answer explanation

The phrase 'Two times a number' translates to '2x', and 'plus ten' adds 10, resulting in '2x + 10'. Setting this equal to 'twenty' gives the equation '2x + 10 = 20', which is the correct choice.

What is the first step in solving the following equation?
3x - 5 = 20

• multiply both sides by 5

• add 5 to both sides

• divide both sides by 5

• subtract both sides by 5

Answer explanation

To isolate the variable x in the equation 3x - 5 = 20, the first step is to eliminate the -5. This is done by adding 5 to both sides, resulting in 3x = 25, which simplifies the equation for further solving.

3c + 5 = 23

• c = 3

• c = 6

• c = 7

• c = 18

Answer explanation

To solve for c, subtract 5 from both sides: 3c = 18. Then, divide by 3: c = 6. Thus, the correct answer is c = 6.

What is the first step to solve this equation:
11 - 3x = 44

• Add 3 to both sides

• Subtract 11 from both sides

• Add 11 to both sides

• Divide 3 on both sides.

Answer explanation

To isolate the variable x, the first step is to eliminate the constant on the left side. Subtracting 11 from both sides simplifies the equation to -3x = 33, making it easier to solve for x.

Is x = 6 a solution to 6x - 12 = 24?

• Yes

• No

Answer explanation

To check if x = 6 is a solution, substitute 6 into the equation: 6(6) - 12 = 36 - 12 = 24. Since both sides equal 24, x = 6 is indeed a solution. Therefore, the answer is Yes.

An expression with an equal sign is called an...

• inequality

• formula

• equation

Answer explanation

An expression with an equal sign indicates that two values are the same, which defines an equation. In contrast, inequalities express a relationship where values are not necessarily equal.

To solve the equation so the variable is BY ITSELF on one side of the equal sign means..

• Add the variable to both sides of the equation.

• Isolate

• Multiply both sides by the same number.

Answer explanation

To solve the equation and have the variable by itself, you need to 'isolate' it. This means performing operations to get the variable on one side of the equation, separate from other terms.

• SUBTRACT 10 to both sides

• ADD 20 to both sides

• ADD 10 to both sides

Answer explanation

To isolate x in the equation x + 10 = 20, you need to eliminate the +10. This is done by subtracting 10 from both sides, resulting in x = 10. Therefore, the correct choice is to SUBTRACT 10 to both sides.

In the following equation, decide if you need to ADD or SUBTRACT from both sides: 5x-4=36

• MULTIPLY 4

• IGNORE 4

• ADD 4

Answer explanation

To isolate the variable x, we need to eliminate the -4 on the left side. We do this by adding 4 to both sides of the equation. Therefore, the correct choice is to ADD 4.