Solve the following:(2 points)

Question

ax−44<15
ax+15=44

Answer 1

To solve the given inequalities and equation, we need to isolate the variable \(x\) in each case.

1. Inequality: \(ax - 44 < 15\)

   First, add 44 to both sides: \[ ax < 15 + 44 \] \[ ax < 59 \]

   Now, divide both sides by \(a\) (assume \(a \neq 0\)): \[ x < \frac{59}{a} \quad \text{if } a > 0 \] or \[ x > \frac{59}{a} \quad \text{if } a < 0 \]

2. Equation: \(ax + 15 = 44\)

   Subtract 15 from both sides: \[ ax = 44 - 15 \] \[ ax = 29 \]

   Now, divide both sides by \(a\) (again assuming \(a \neq 0\)): \[ x = \frac{29}{a} \]

Summary:

• For the inequality \(ax - 44 < 15\):

  • If \(a > 0\), \(x < \frac{59}{a}\)
  • If \(a < 0\), \(x > \frac{59}{a}\)

• For the equation \(ax + 15 = 44\):

  • \(x = \frac{29}{a}\)

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