Solve the equation and inequality for x(2 points)
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ax+15=44
: Response area
ax−44<15
:
Response area
To solve the equation ax + 15 = 44 for x, we can follow these steps:
Step 1: Subtract 15 from both sides of the equation.
ax + 15 - 15 = 44 - 15
ax = 29
Step 2: Divide both sides of the equation by a.
ax/a = 29/a
x = 29/a
To solve the inequality ax - 44 < 15 for x, we can follow these steps:
Step 1: Add 44 to both sides of the inequality.
ax - 44 + 44 < 15 + 44
ax < 59
Step 2: Divide both sides of the inequality by a. Make sure to consider the cases where a is positive or negative.
If a > 0:
ax/a < 59/a
x < 59/a
If a < 0:
(ax/a)(a/a) < (59/a)(a/a)
(-x) < (-59/a)
Multiply both sides by -1 to reverse the inequality:
x > 59/a
So, the solutions to the equation and inequality depend on the value of a.
To solve the equation ax + 15 = 44 for x, we need to isolate x on one side of the equation.
1. Subtract 15 from both sides of the equation:
ax + 15 - 15 = 44 - 15
Simplifying, we have:
ax = 29
2. To solve for x, divide both sides of the equation by a:
ax/a = 29/a
The "a" term cancels out on the left side, leaving us with:
x = 29/a
To solve the inequality ax - 44 < 15 for x, we follow similar steps:
1. Add 44 to both sides of the inequality:
ax - 44 + 44 < 15 + 44
Simplifying, we have:
ax < 59
2. To solve for x, divide both sides of the inequality by a (assuming a is positive):
(ax)/a < 59/a
The "a" term cancels out on the left side, leaving us with:
x < 59/a
So, the solutions for x in the equation and inequality are:
For the equation ax + 15 = 44: x = 29/a
For the inequality ax - 44 < 15: x < 59/a