Equations with No Solutions

Explore linear equations that result in no possible solutions, understanding the algebraic conditions that lead to such outcomes.

Grade 10 Math AlgebraEquations with No Solutions

Use This Worksheet

Includes

2 Short AnswerMultiple ChoiceFill in the BlanksTrue / FalseCustom

Standards

CCSS.MATH.CONTENT.HSA.REI.B.3

Topics

algebraequationsno solutiongrade 10

8 sections · Free to use · Printable

← More Math worksheets for Grade 10

Equations with No Solutions

Name:

Date:

Score:

Read each question carefully and follow the instructions to solve the problems. Show all your work for full credit.

1. Explain in your own words what it means for an equation to have 'no solution'.

2. Which of the following equations has no solution?

3x + 5 = 3x + 5

2x - 7 = 5x + 2

4(x + 1) = 4x + 5

6x - 1 = 2x + 7

3. An equation has no solution if, after simplifying, you arrive at a statement that is always (e.g., 5 = 7).

4. When solving an equation, if the variable terms on both sides of the equal sign cancel out and the remaining constants are not equal, the equation has .

5. The equation 7x - 3 = 7x + 10 has a solution.

True

False

6. Solve the equation: 5(2x - 3) = 10x + 7. Does it have a solution? Explain.

7. Consider the equation: x + 2 = x + 5. If we imagine both sides of the equation as weights on a balance scale, what would happen if you tried to balance them? Explain why this illustrates an equation with no solution.