200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 Solving Equations Solving Literal Equations Solving.

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Presentation transcript:

Solving Equations Solving Literal Equations Solving Absolute Value Equations & Inequalities Solving Inequalities Word Problems

Solving Equations - $100 Solve the equation. 4(6 – 3x) – (x – 8) = 3(1 – 5x)

4(6 – 3x) – (x – 8) = 3(1 – 5x) 24 – 12x – x + 8 = 3 – 15x 32 – 13x = 3 – 15x 2x = -29 x = -29/2 or -14½ Solving Equations - $100

Solving Equations - $200 Solve the equation.

Solving Equations - $200 40x – 3 = 30x x 40x – 3 = 40x = 8 No Solution

Solving Equations - $300 Solve the equation.

Solving Equations - $300 4(x – 5) – 3(3x + 2) = 2(7 – 2x) 4x – 20 – 9x – 6 = 14 – 4x -5x – 26 = 14 – 4x -x = 40 x = -40

Solving Equations - $400 Solve the equation. 2[5x + (x – 3) 2 ] = 3x(x + 5) – x

2[5x + (x – 3) 2 ] = 3x(x + 5) – x [5x + x 2 – 6x + 9] = 3x x – x [x 2 – x + 9] = 2x x x 2 – 2x + 18 = 2x x x = 0 x = 0 Solving Equations - $400

Solving Equations - $500 Solve the equation.

2 + 12x – 9x + 2 = 3x x = 3x + 4 All REAL Numbers Solving Equations - $500

Solve for l. V = lwh Solving Literal Equations - $100

V = lwh Solving Literal Equations - $100

Solve for x. 2x + 3y = 10 Solving Literal Equations - $200

2x + 3y = 10 2x = -3y + 10 x = -3y or x = -3y Solving Literal Equations - $200

Solve for n. L = a + (n – 1) d Solving Literal Equations - $300

L = a + (n – 1) d L – a = (n – 1)d L – a = n – 1 d L – a + 1 = n OR L – a + d = n d d Solving Literal Equations - $300

Solve for z. pz – 4z = k Solving Literal Equations - $400

pz – 4z = k z(p – 4) = k z = k _ (p – 4)

Solve for g. rg + m = 2(g – 1) Solving Literal Equations - $500

rg + m = 2(g – 1) rg + m = 2g – 2 rg – 2g = -m – 2 g(r – 2) = -m – 2 g = -m – 2 r - 2

Solving Absolute Value Equations & Inequalities- $100 Solve the equation. |17 – 3x| = 43

Solving Absolute Value Equations & Inequalities- $100 |17 – 3x| = – 3x = 43 OR 17 – 3x = x = 26- 3x = -60 x = - 26/3OR x = 20

Solve the equation. 3 |4x + 5| - 6 = 42 Solving Absolute Value Equations & Inequalities- $200

3 |4x + 5| - 6 = 42 3 |4x + 5| = 48 |4x + 5| = 16 4x + 5 = 16 OR 4x + 5 = -16 4x = 11 4x = - 21 x = 11/4 OR x = -21/4

Solve and graph the inequality. |6x – 11| < 25 Solving Absolute Value Equations & Inequalities- $300

|6x – 11| < 25 Find the critical values. |6x – 11| = 25 6x – 11 = 25 6x – 11 = -25 x = 6 x = -7/3 Test values within the intervals. x -7/3 6-7/3 ●●

Solve and graph the inequality. 7 |8 – 2x| > 63 Solving Absolute Value Equations & Inequalities- $400

7 |8 – 2x| > 63 |8 – 2x| > 9 Find the critical values. |8 – 2x| = 9 8 – 2x = 9 8 – 2x = -9 x = -1/2 x = 17/2 Test values within the intervals. x 17/2 17/2-1/2 ○○

Solve and graph the inequality. ½ |5x – 1| - 7 < 10 Solving Absolute Value Equations & Inequalities- $500

½ |5x – 1| - 7 < 10 ½ |5x – 1| < 17 |5x – 1| < 34 Find the critical values. |5x – 1| = 34 5x – 1 = 34 5x – 1 = -34 x = 7 x = -33/5 Test values within the intervals. x -33/ /5 ○ ○

Solving Inequalities- $100 Solve and graph the inequality. 4m – 11 < 8m + 7

4m – 11 < 8m m < 18 m > -9/2 ( m > -4½ ) Solving Inequalities- $100 -9/2 ●

Solve and graph the inequality. -3(k – 2) + 9 > 2(k – 5) Solving Inequalities- $200

-3(k – 2) + 9 > 2(k – 5) -3k > 2x – k + 15 > 2x – k > - 25 k < 5 5 ○

Solve and graph the inequality. 4 < 2y – 2 < 10 Solving Inequalities- $300

4 < 2y – 2 < 10 6 < 2y < 12 3 < y < 6 63 ○ ○

Solve and graph the inequality. 3n Solving Inequalities- $400

3n n < 2 OR n < 4 n < 2/3 OR n < 4 n < 4 4 ○

Solve the and graph inequality. 3w w Solving Inequalities- $500

3w – w 3w - 1 w -5 All REAL Numbers

Word Problems - $100 Seven less than triple a number is 9 more than the number. Find the number.

Word Problems - $100 3x – 7 = 9 + x x = 8 the number is 8

Find 3 consecutive integers such that the difference of the squares of the last and first is equal to the product of 5 and the second integer. Word Problems - $200

(x + 2) 2 – x 2 = 5(x + 1) x 2 + 4x + 4 – x 2 = 5x + 5 4x + 4 = 5x + 5 -x = 1 x = -1 x = -1, x + 1 = 0, and x + 2 = 1 Word Problems - $200

The perimeter of a rectangular park is 624 yards. If the length is 8 yards more than 3 times the width, find the dimensions of the park. Word Problems - $300

2w + 2(3w + 8) = 624 2w + 6w + 16 = 624 8w + 16 = 624 8w = 608 w = 76 yards 3w + 8 = 236 yards park is 76 yards x 236 yards Word Problems - $300

Jim and Joe started on trips from San Francisco traveling in opposite directions. Jim traveled 15 km/h faster than Joe. After 4 hours, they were 420 km apart. How fast was each person traveling? Word Problems - $400

4x + 4(15 + x) = 420 4x x = 420 8x + 60 = 420 8x = 360 x = 45 km/h 15 + k = 60 km/h Joe – 45 km/h Jim – 60 km/h Word Problems - $400

A coin bank contains twice as many nickels as quarters, three times as many pennies as quarters, and no dimes. If the bank contains $7. 60, how many of each coin does it contain? Word Problems - $500

2x(.05) + x(.25) + 3x(.01) = x +.25x +.03x = x = 7.60 x = quarters, 40 nickels, and 60 pennies Word Problems - $500