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 ∞.

Question

Johnathon Sawyer

Mathematics

18 May, 10:29

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 ∞.

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Answers (1)

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Shannon · 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]