Solve −4x + 2 > 13
Linear inequality, worked out line by line the way a teacher would write it.
Answer
| Solution | x < −11/4 |
| Interval notation | (−∞, −11/4) |
Step-by-step solution
4 steps-
1 Given- 4 x + 2 > 13
Solve for x.
-
2 Subtract 2 from both sides
Like an equation, an inequality stays true when the same amount is added to or subtracted from both sides. Only multiplying or dividing by a negative number needs extra care: it reverses the sign.
- 4 x > 11Move the constant terms to the right.
-
3 Divide both sides by -4 and reverse the inequality sign
Multiplying or dividing by a negative number reverses the order of numbers: 2 < 3, but −2 > −3. So the inequality sign has to be turned around to stay true.
x < - \frac{11}{4}Multiplying or dividing both sides by a negative number reverses the inequality.
-
4 Solutionx < - \frac{11}{4}\qquad \left( -\infty, - \frac{11}{4} \right)
Check with test values
| x | Left side | Right side | Holds? |
|---|---|---|---|
| −3 | 14 | 13 | ✓ true |
| −2 | 10 | 13 | ✗ false |
Open this problem in the solver
Change a number or try your own problem: the solver works it out the same way, with a graph and hint mode.