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Solving Linear Equations Basics
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Solving Linear Equations Basics
Solve each equation by keeping both sides balanced. Show your steps for the solve-and-check questions. You can check a solution by substituting it for x.
Warm up: one-step equations
Undo the operation acting on x. Write the value that makes each equation true.
1.A number plus 9 equals 23. Solve x + 9 = 23.
2.Solve x − 6 = 11. Which operation should you use first to isolate x?
- Add 6 to both sides
- Subtract 6 from both sides
- Multiply both sides by 6
- Divide both sides by 6
3.A pack has x markers. Four equal packs contain 36 markers altogether. Solve 4x = 36.
4.A ribbon of length x inches is cut into 5 equal pieces, each 7 inches long. Solve x ÷ 5 = 7.
Two-step challenges
Undo addition or subtraction first, then undo multiplication or division. Apply each operation to both sides.
5.Solve 3x + 4 = 19. Show both inverse-operation steps.
6.A game score starts at x points, then earns 5 points in each of 4 rounds. The final score is 29. Solve x + 4(5) = 29.
7.Solve 5x − 8 = 27. Include the value of x.
8.Solve 6 − 2x = 0. Be careful: the coefficient of x is negative.
9.True or false: x = 4 is a solution to 2x + 3 = 11. Substitute 4 to check.
TrueFalse
10.Find and fix the mistake in this work for 2x + 7 = 17: “Subtract 7 to get 2x = 10. Then subtract 2, so x = 8.” State the correct answer.
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