Solving Linear Equations and Inequalities

To solve an equation, use ____________ operations to isolate the variable. Word bank: graph, inverse, flips, letter, value.

• inverse

• graph

• flips

• letter

Answer explanation

To isolate the variable in an equation, you use inverse operations. These operations, such as addition and subtraction or multiplication and division, effectively 'undo' each other, allowing you to solve for the variable.

Tags

CCSS.7.EE.B.4A

Fill in the Blank: Fill in the blank with the correct words. The solution to an inequality is often represented on a ____________.

• graph

• inverse

• flips

• letter

Answer explanation

The solution to an inequality is often represented on a graph, which visually shows the range of values that satisfy the inequality. The other options do not relate to representing solutions to inequalities.

Tags

CCSS.6.EE.B.8

When multiplying or dividing both sides of an inequality by a negative number, the inequality sign ____________. Word bank: graph, inverse, flips, letter, value.

• flips

• remains unchanged

• gets inverted

• stays the same

Answer explanation

When you multiply or divide both sides of an inequality by a negative number, the inequality sign flips. This is a crucial rule in solving inequalities to maintain the correct relationship between the values.

Tags

CCSS.6.EE.B.8

Fill in the Blank: Fill in the blank with the correct words. In a linear equation, the variable is usually denoted by a ____________. Word bank: graph, inverse, flips, letter, value.

• letter

• graph

• inverse

• value

Answer explanation

In a linear equation, the variable is typically represented by a 'letter', such as x or y. This distinguishes it from other terms like 'graph' or 'value', which do not denote the variable itself.

Tags

CCSS.6.EE.A.2B

Fill in the Blank: Fill in the blank with the correct words. Solving an equation involves finding the ____________ of the variable. Word bank: graph, inverse, flips, letter, value.

• value

• graph

• inverse

• letter

Answer explanation

Solving an equation means determining the 'value' of the variable that makes the equation true. The other options do not accurately describe this process.

Tags

CCSS.7.EE.B.4A

What is the first step in solving the equation (3x + 5 = 20)?

• Multiply both sides by 3

• Subtract 5 from both sides

• Add 5 to both sides

• Divide both sides by 3

Answer explanation

To isolate x in the equation 3x + 5 = 20, the first step is to eliminate the constant term. Subtracting 5 from both sides simplifies the equation to 3x = 15, making it easier to solve for x.

Tags

CCSS.7.EE.B.4A

In the inequality (4x - 7 < 9), what operation should be performed first to begin isolating (x)?

• Add 7 to both sides

• Subtract 7 from both sides

• Multiply both sides by 4

• Divide both sides by 4

Answer explanation

To isolate x in the inequality 4x - 7 < 9, you should first eliminate the -7. Adding 7 to both sides simplifies the inequality to 4x < 16, making it easier to solve for x.

Tags

CCSS.7.EE.B.4B

How do you check if a solution to an equation is correct?

• Substitute the solution back into the original equation

• Rewrite the equation

• Graph the equation

• Use a calculator to check

Answer explanation

To verify a solution, substitute it back into the original equation. If both sides of the equation are equal, the solution is correct. This method directly checks the validity of the solution.

Tags

CCSS.6.EE.B.5

If you have the inequality (x/3 > 2), what is the solution for (x)?

• (x > 6)

• (x > 5)

• (x > 4)

• (x > 3)

Answer explanation

To solve the inequality x/3 > 2, multiply both sides by 3, yielding x > 6. Thus, the correct solution is (x > 6).

Tags

CCSS.6.EE.B.8

Which of the following represents a linear equation?

• (2x + 3y = 6)

• (3x + 4 = 7)

Answer explanation

The equation (2x + 3y = 6) is linear because it can be expressed in the form Ax + By = C, where A, B, and C are constants. The other options involve non-linear terms, making them not linear equations.

Tags

CCSS.8.F.A.3