Solve 5x-2/3+2x-1/2leq7

$$\frac { 5 x - 2 } { 3 } + \frac { 2 x - 1 } { 2 } \leq 7$$

Solve for x

$$x\leq \frac{49}{16}$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

$$2\left(5x-2\right)+3\left(2x-1\right)\leq 42$$

Use the distributive property to multiply 2 by 5x-2.

$$10x-4+3\left(2x-1\right)\leq 42$$

Use the distributive property to multiply 3 by 2x-1.

$$10x-4+6x-3\leq 42$$

Combine 10x and 6x to get 16x.

$$16x-4-3\leq 42$$

Subtract 3 from -4 to get -7.

$$16x-7\leq 42$$

Add 7 to both sides.

$$16x\leq 42+7$$

Add 42 and 7 to get 49.

$$16x\leq 49$$

Divide both sides by 16. Since 16 is positive, the inequality direction remains the same.

$$x\leq \frac{49}{16}$$