Chapter 1 Chapter Test 47Chapter Test
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Solve the equation. Justify each step. Check your solution.1. x 7 15 2. 2 — 3 x + 5 3 3. 11x + 1 1 + xSolve the equation.4. 2 x 3 5 7 5. 2x 19 4x + 1 6. 2 + 5x 7 3x 9 + 2x7. 3(x + 4) 1 7 8. 20 + 2x 4x + 4 9. 1 — 3 (6x + 12) 2(x 7) 19Describe the values of c for which the equation has no solution. Explain your reasoning.10. 3x 5 3x c 11. x 7 c12. A safety regulation states that the minimum height of a handrail is 30 inches. The maximum height is 38 inches. Write an absolute value equation that represents the minimum and maximum heights.13.The perimeter P (in yards) of a soccer  eld is represented by the formula P 2ℓ+ 2w, whereℓ is the length (in yards) and w is the width (in yards).a. Solve the formula for w.b. Find the width of the eld.c. About what percent of the eld is inside the circle?14. Your car needs new brakes. You call a dealership and a local mechanic for prices.Cost of partsLabor cost per hourDealership$24$99Local Mechanic$45$89a. After how many hours are the total costs the same at both places? Justify your answer.b. When do the repairs cost less at the dealership? at the local mechanic? Explain.15. Consider the equation 4x + 20 6x. Without calculating, how do you know that x 2 is an extraneous solution?16. Your friend was solving the equation shown and was confused by the result “8 8.” Explain what this result means.4(y 2) 2y 6y 8 4y 4y 8 2y 6y 8 4y 2y 8 2y 88 8 100 ydP 330 yd10 yd