Evaluate the expression if w = -4, x = 2, y = ½, and z = |6 + z| - |7| Original problem. |6 + (-6)| - |7| Substitute values for the variables.

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Presentation transcript:

Evaluate the expression if w = -4, x = 2, y = ½, and z = -6. 2. |6 + z| - |7| Original problem. |6 + (-6)| - |7| Substitute values for the variables. |0| - |7| Simplify inside each absolute value. 0 – 7 = -7 Take absolute values and simplify. Final Answer is -7. 6. |7 – x| + |3x| Original problem. |7 – 2| + |3(2)| Substitute values for the variables. |5| - |6| Simplify inside each absolute value. 5 + 6 = 11 Take absolute values and simplify. Final Answer is 11.

Evaluate the expression if w = -4, x = 2, y = ½, and z = -6. 10. 5|w| + 2|z – 3y| Original problem. 5|-4| + 2|-6 – 3(1/2)| Substitute values for the variables. 5|-4| + 2|-7 ½ | Simplify inside each absolute value. 5(4) + 2(-15/2) = 5 Take absolute values and simplify. Final Answer is 5. 12. 3|wx| + (1/4)|4x + 8y| Original problem. 3|(-4)(2)| + (1/4)|4(2) + 8(1/2)| Substitute values for the variables. 3|-8| + (1/4)|12| Simplify inside each absolute value. 24 + 3 = 27 Take absolute values and simplify. Final Answer is 27.

Evaluate the expression if w = -4, x = 2, y = ½, and z = -6. 18. |xyz| + |wxz| Original problem. |(2)(1/2)(-6)| + |(-4)(2)(-6)| Substitute values for the variables. |-6| + |48| Simplify inside each absolute value. 6 + 48 = 54 Take absolute values and simplify. Final Answer is 54. 22. |yz – 4w| - w Original problem. |(1/2)(-6) – 4(-4)| - (-4) Substitute values for the variables. |13| - (-4) Simplify inside each absolute value. 13 + 4 = 17 Take absolute values and simplify. Final Answer is 17.

Solve the equation. Check your solutions. |15 – 2k| = 45 Original Equation. Since Absolute Value bars are isolated, just set up two equations to be solved. One that is a positive answer the other a negative answer. a. 15 – 2k = 45 b. 15 – 2k = -45 15 – 2k = 45 move 15. -2k = 30 move -2. k = -15 Solution. 15 – 2k = -45 move 15. -2k = -60 move -2. k = 30 Solution. Check the solutions k = -15 and 30 into original equation. k = -15 k = 30 |15 – 2k| = 45 |15 – 2k| = 45 |15 – 2(-15)| = 45 |15 – 2(30)| = 45 |45| = 45 yes |-45| = 45 yes Final Answer is k = -15 and 30.

Solve the equation. Check your solutions. 8. |8 + 5a| = 14 – a Original Equation. Since Absolute Value bars are isolated, just set up two equations to be solved. One that is a positive answer the other a negative answer. a. 8 + 5a = 14 – a b. 8 + 5a = -(14 – a) 8 + 5a = 14 – 1a move -1a. 8 + 6a = 14 move 8. 6a = 6 move 6. a = 1 solution. 8 + 5a = -14 + 1a move 1a. 8 + 4a = -14 move 8. 4a = -22 move 4. a = -22/4 = -11/2 solution. Check the solutions a = 1 and -11/2 into original equation. k = 1 k = -11/2 |8 + 5a| = 14 – a |8 + 5a| = 14 – a |8 + 5(1)| = 14 – 1 |8 + 5(-11/2)| = 14 – (-11/2) |13| = 13 yes |-15/2| = 15 1/2 yes Final Answer is a = 1 and -11/2.

Solve the equation. Check your solutions. 10. |3x – 1| = 2x + 11 Original Equation. Since Absolute Value bars are isolated, just set up two equations to be solved. One that is a positive answer the other a negative answer. a. 3x – 1 = 2x + 11 b. 3x – 1 = -(2x + 11) 3x – 1 = 2x + 11 move 2x. x – 1 = 11 move 1. x = 12 x = 12 solution. 3x – 1 = -2x – 11 move -2x. 5x – 1 = -11 move 1. 5x = -10 move 5. x = -2 solution. Check the solutions x = 12 and -2 into original equation. k = 12 k = -2 |3x – 1| = 2x + 11 |3x – 1| = 2x + 11 |3(12) – 1| = 2(12) + 11 |3(-2) – 1| = 2(-2) + 11 |35| = 35 yes |-7| = 7 yes Final Answer is k = 12 and -2.

Solve the equation. Check your solutions. 12. 40 – 4x = 2|3x – 10| Original Equation. Since Absolute Value bars are not isolated, divide each side by 2 to isolate the bars. Then set up two equations to be solved. a. 20 – 2x = 3x – 10 b. 20 – 2x = -(3x – 10) 20 – 2x = 3x – 10 move 3x. 20 – 5x = -10 move 20. -5x = -30 move -5. x = 6 solution. 20 – 2x = -3x + 10 move -3x. 20 + 1x = 10 move 20. 1x = -10 move 1. x = -10 solution. Check the solutions x = 6 and -10 into original equation. k = 6 k = -10 40 – 4x = 2|3x – 10| 40 – 4x = 2|3x – 10| 40 – 4(6) = 2|3(6) – 10| 40 – 4(-10) = 2|3(-10) – 10| 16 = 2(8) yes 80 = 2(40) yes Final Answer is k = 6 and -10.

Solve the equation. Check your solutions. 14. |4b + 3| = 15 – 2b Original Equation. Since Absolute Value bars are isolated, just set up two equations to be solved. One that is a positive answer the other a negative answer. a. 4b + 3 = 15 – 2b b. 4b + 3 = -(15 – 2b) 4b + 3 = 15 – 2b move -2b. 6b + 3 = 15 move 3. 6b = 12 move 6. b = 2 solution. 4b + 3 = -15 + 2b move 2b. 2b + 3 = -15 move 3. 2b = -18 move 5. b = -9 solution. Check the solutions x = 2 and -9 into original equation. k = 2 k = -9 |4b + 3| = 15 – 2b |4b + 3| = 15 – 2b |4(2) + 3| = 15 – 2(2) |4(-9) + 3| = 15 – 2(-9) |11| = 11 yes |-33| = 33 yes Final Answer is k = 2 and -9.

Solve the equation. Check your solutions. 16. |16 – 3x| = 4x - 12 Original Equation. Since Absolute Value bars are isolated, just set up two equations to be solved. One that is a positive answer the other a negative answer. a. 16 – 3x = 4x – 12 b. 16 – 3x = -(4x – 12) 16 – 3x = 4x – 12 move 4x. 16 – 7x = 12 move 16. -7x = -4 move -7. x = 4/7 solution. 16 – 3x = -4x + 12 move -4x. 16 + 1x = 12 move 16. 1x = -4 move 1. b = -1/4 solution. Check the solutions x = 4/7 and -1/4 into original equation. k = 4/7 k = -1/4 |16 – 3x| = 4x – 12 |16 – 3x| = 4x – 12 |16 – 3(4/7)| = 4(4/7) – 12 |16 – 3(-1/4)| = 4(-1/4) – 12 |100/7| = -68/7 no |16 3/4| = -13 no Final Answer is No Solution.