Question
Solve the inequality
Solve for x
−4≤x≤3
Alternative Form
x∈[−4,3]
Evaluate
∣4x+2∣+6≤20
Calculate the absolute value
More Steps
Evaluate
∣4x+2∣
Rewrite the expression
∣2(2x+1)∣
Rewrite the expression
2∣2x+1∣
2∣2x+1∣+6≤20
Move the expression to the left side
2∣2x+1∣+6−20≤0
Subtract the numbers
2∣2x+1∣−14≤0
Rewrite the expression
2∣2x+1∣≤14
Divide both sides
22∣2x+1∣≤214
Divide the numbers
∣2x+1∣≤214
Divide the numbers
More Steps
Evaluate
214
Reduce the numbers
17
Calculate
7
∣2x+1∣≤7
Separate the inequality into 2 possible cases
{2x+1≤72x+1≥−7
Solve the inequality for x
More Steps
Evaluate
2x+1≤7
Move the constant to the right side
2x≤7−1
Subtract the numbers
2x≤6
Divide both sides
22x≤26
Divide the numbers
x≤26
Divide the numbers
More Steps
Evaluate
26
Reduce the numbers
13
Calculate
3
x≤3
{x≤32x+1≥−7
Solve the inequality for x
More Steps
Evaluate
2x+1≥−7
Move the constant to the right side
2x≥−7−1
Subtract the numbers
2x≥−8
Divide both sides
22x≥2−8
Divide the numbers
x≥2−8
Divide the numbers
More Steps
Evaluate
2−8
Reduce the numbers
1−4
Calculate
−4
x≥−4
{x≤3x≥−4
Solution
−4≤x≤3
Alternative Form
x∈[−4,3]
Show Solution