Classwork - Multi-Step Variable Both Side with Explanations

Solve the equation: 3x + 5 = 2x - 7

• -6

• 10

• 4

• -12

Answer explanation

To solve the equation, subtract 2x from both sides to get x + 5 = -7. Then, subtract 5 from both sides to get x = -12. Therefore, the correct answer is -12.

What is the first step to solve an equation with variables on both sides?

• Multiply both sides by a common denominator

• Combine like terms on both sides

• Isolate the variable on one side

• Simplify both sides of the equation

Answer explanation

The first step to solve an equation with variables on both sides is to simplify both sides of the equation. This allows for easier manipulation and isolation of the variable.

Combine like terms in the equation: 4x + 2 - 3x - 5

• -x + 3

• x - 3

• x + 3

• -x - 3

Answer explanation

To combine like terms, we add or subtract the coefficients of the same variable. In this equation, 4x and -3x are like terms, so we subtract their coefficients to get x. Similarly, 2 and -5 are like terms, so we subtract their coefficients to get -3. Therefore, the equation simplifies to x - 3. This matches the correct choice.

Simplify the expression using the distributive property: 2(3x + 4)

• 6x + 4

• 6x + 8

• 6x + 12

• 6x - 8

Answer explanation

To simplify the expression 2(3x + 4) using the distributive property, distribute 2 to both terms inside the parentheses. This gives us 6x + 8. Therefore, the correct choice is 6x + 8.

Solve the equation: 2(2x - 3) = 4x + 5

• No solution

• x = 0

• x = -1

• x = 2

Answer explanation

The equation simplifies to 4x - 6 = 4x + 5. Subtracting 4x from both sides gives -6 = 5, which is not true. Therefore, there is no solution to the equation.

What is the next step after combining like terms in an equation with variables on both sides?

• Isolate the variable on one side of the equation by performing inverse operations.

• Multiply or divide both sides by a variable

• Add or subtract a constant from both sides

• Combine unlike terms

Answer explanation

The next step after combining like terms is to isolate the variable by performing inverse operations.

Combine like terms in the equation: 5x - 3 + 2x + 7

• 7x + 4

• 3x + 4

• 7x + 10

• 10x + 4

Answer explanation

To combine like terms, add the coefficients of x. The correct choice is 7x + 4, as it combines the x terms and simplifies the constants.

Simplify the expression using the distributive property: 3(2x - 5)

• 5 - 2x

• 6x + 15

• 6x - 15

• 3x - 15

Answer explanation

To simplify the expression 3(2x - 5) using the distributive property, distribute 3 to both terms inside the parentheses. This gives us 6x - 15. Therefore, the correct choice is 6x - 15.

Solve the equation: 4(3x - 2) = 2(5x + 1)

• x = 4

• x = 2

• x = 5

• x = 3

Answer explanation

To solve the equation, distribute and simplify both sides. Combine like terms and isolate the variable. The correct choice is x = 5.

What is the final step to solve an equation with variables on both sides?

• Multiply both sides by a common denominator

• Simplify and combine like terms on both sides

• Isolate the variable on one side

• Distribute the terms on both sides

Answer explanation

The final step to solve an equation with variables on both sides is to simplify and combine like terms on both sides. This step helps isolate the variable on one side and makes it easier to solve the equation.