How do you solve the compound inequalities #−22 −5x − 7 =−3#?

Question

How do you solve the compound inequalities #−22 > −5x − 7 >=−3#?

Avery Alexander · Accepted Answer

I will assume that the leading - before the 22 is a hyphen and not a minus sign. If it were a minus sign there would be no solution.

You can apply any of the following operations to all parts of such a compound inequality retaining its truth: (1) Add or subtract a constant. (2) Multiply or divide by a positive number. (3) Multiply or divide by a negative number and reverse the signs.

Start by adding 7 to all parts to get: #29 > -5x >= 4#

Divide by 5: #29/5 > -x >= 4/5#

Multiply by -1 and reverse the signs: #-29/5 < x <= -4/5#

Or in decimal notation: #-5.8 < x <= -0.8#

Avery Alexander · Answer

undefined To solve the compound inequality $ -22 > -5x - 7 \geq -3 $, follow these steps: 1. Add 7 to all parts of the compound inequality: $$ -22 + 7 > -5x - 7 + 7 \geq -3 + 7 $$ 2. Simplify: $$ -15 > -5x \geq 4 $$ 3. Divide all parts by -5. Since you are dividing by a negative number, the direction of the inequalities will reverse: $$ \frac{-15}{-5} < \frac{-5x}{-5} \leq \frac{4}{-5} $$ 4. Simplify: $$ 3 < x \leq -\frac{4}{5} $$ So, the solution to the compound inequality is $ 3 < x \leq -\frac{4}{5} $.

How do you solve the compound inequalities #−22 &gt; −5x − 7 &gt;=−3#?

How do you solve the compound inequalities #−22 > −5x − 7 >=−3#?