# Math Hw Inequality Help?

+1 vote

1 0.4z ≧ 9.65 + 0.5z

2. 4/11c - 5/13c ≤ 3

3. Frank is trying to save money to buy a car. The car he wants costs \$16,795. He has saved \$11,590. He is planning on saving money each month by working over the next year. Solve the inequality 16,795 ≤ 11,590 + 12m to find the least amount of money he needs to save each month.

+1 vote

1) 0.4z ≥ 9.65 + 0.5z

Apply subtraction property of inequality: Subtract 9.65 from each side.

0.4z − 9.65 ≥ 9.65 + 0.5z − 9.65

0.4z − 9.65 ≥ 0.5z                         (Simplify)

0.4z − 9.65 − 0.4z ≥ 0.5z − 0.4z  (Subtract 0.4z from each side)

− 9.65 ≥ 0.1z                                 (Simplify)

− 9.65/0.1 ≥ 0.1z/0.1                     (Divide each side by 0.1)

− 96.5 ≥ z                                      (Simplify)

z ≤ − 96.5

Graph the solution set on a number line.

Note: A dot means that this point is included in the solution set.

The inequality solution set is {z|z ≤ − 96.5}.

+1 vote

2) 4/11c - 5/13c ≤ 3

LCM of 11 and 13 is 143.

Rewrite the inequality using LCM.

(4×13/11×13)c - (5×11/13×11)c ≤ 3

(52/143)c – (55/143)c ≤ 3          (Simplify)

Dinominators are same subtract the numarators.

(52 – 55/143)c ≤ 3

( – 3/143)c ≤ 3                           (Subtract: 52 – 55 = – 3)

( – 3/143)c×143 ≤ 3×143           (Multiply each side by 143)

– 3c ≤ 429                                  (Simplify)

– 3c/3 ≤ 429/3                            (Divide each side by 3)

– c ≤ 143                                    (Divide: 429/3 = 143)

–(– c) ≥ –143                             (Multiply each side by negative one and flip the symbol)

c ≥ –143                                     (Product of two same signs is positive)

Graph the solution on a number line.

Note: A dot means that this point is included in the solution set.

The inequality solution set is {c|c ≥ –143}.

3). 16795 < 11560 + 12m

Apply subtraction property of inequality: Subtract 11560 from each side.

16795 - 11590 < 11560 + 12m - 11560

5205 < 12m                                   (Simplify)

5205 / 12 < 12m / 12                     (Divide each side by 12)

433.75 < m                                   (Simplify)

m >  433.75

Graph the solution set on a number line.

Note: A dot means that this point is included in the solution set.

The inequality solution set is {m|m >  433.75 }.

3). 16795 < 11590 + 12m

Apply subtraction property of inequality: Subtract 11590 from each side.

16795 - 11590 < 11590 + 12m - 11590

5205 < 12m                                   (Simplify)

5205 / 12 < 12m / 12                     (Divide each side by 12)

433.75 < m                                   (Simplify)

m >  433.75

Graph the solution set on a number line.

Note: A dot means that this point is included in the solution set.

The inequality solution set is {m|m >  433.75 }.