Solve for x
x\geq -\frac{11}{4}
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3\left(2x-1\right)-2\left(5x+1\right)\leq 6
Multiply both sides of the equation by 6, the least common multiple of 2,3. Since 6 is positive, the inequality direction remains the same.
6x-3-2\left(5x+1\right)\leq 6
Use the distributive property to multiply 3 by 2x-1.
6x-3-10x-2\leq 6
Use the distributive property to multiply -2 by 5x+1.
-4x-3-2\leq 6
Combine 6x and -10x to get -4x.
-4x-5\leq 6
Subtract 2 from -3 to get -5.
-4x\leq 6+5
Add 5 to both sides.
-4x\leq 11
Add 6 and 5 to get 11.
x\geq -\frac{11}{4}
Divide both sides by -4. Since -4 is negative, the inequality direction is changed.
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Limits
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