Question

Type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numbers. If necessary, use / for the fraction bar(s). The solution set for all real numbers x such that 2x + 3 < 19 and 2x − 3 ≤ -7 is (, ]. Note: If needed, type “-infinity” for -∞ and “infinity” for ∞.

Answer 1

2x + 3 < 19 and 2x − 3 ≤ -7

Solve each inequality

2x + 3 < 19

subtract 3 from both sides

2x  < 16

Divide both sides by 2

x < 8

2x − 3 ≤ -7

Add 3 on  both sides

2x  ≤ -4

Divide both sides by 2

x  ≤ -2

we got  x<8  and x  ≤ -2

When we combine both solutions then we will get

x  ≤ -2

Interval form is (-infinity, -2]