Question

answer: $xleq - 9$ or $xgeq 6$ # solve the inequality then graph the solution. $5x + 7>2x + 4$ and $3x + 3<24 - 4x$

Explanation:

Step1: Solve the first inequality

Subtract \(2x\) and 7 from both sides of \(5x + 7>2x + 4\).
\(5x-2x>4 - 7\), which simplifies to \(3x>-3\). Then divide both sides by 3, getting \(x>- 1\).

Step2: Solve the second inequality

Add \(4x\) to both sides and subtract 3 from both sides of \(3x + 3<24-4x\).
\(3x + 4x<24 - 3\), which simplifies to \(7x<21\). Then divide both sides by 7, getting \(x < 3\).
The intersection of \(x>-1\) and \(x < 3\) is \(-1We draw a number line. Mark points \(-1\) and \(3\) with open circles (because the inequality is strict, \(x
eq - 1\) and \(x
eq3\)) and shade the region between them.

The problem seems to have an incorrect provided answer. If we follow the steps for the given inequalities correctly, the solution of the compound - inequality \(5x + 7>2x + 4\) and \(3x + 3<24-4x\) is \(-1

If we assume there was a mistake in how the problem was written and we were to graph \(x\leq - 9\) or \(x\geq6\):
On a number line, mark \(-9\) with a closed circle (because \(x\) can equal \(-9\) for \(x\leq - 9\)) and shade to the left of \(-9\). Mark 6 with a closed circle (because \(x\) can equal 6 for \(x\geq6\)) and shade to the right of 6.

Answer:

The solution of \(5x + 7>2x + 4\) and \(3x + 3<24-4x\) is \(-1