Solve 5x+46/3leq2(3x-1)

$$\frac { 5 x + 46 } { 3 } \leq 2 ( 3 x - 1 )$$

Solve for x

$$x\geq 4$$

Solution Steps

Multiply both sides of the equation by 3. Since 3 is positive, the inequality direction remains the same.

$$5x+46\leq 6\left(3x-1\right)$$

Use the distributive property to multiply 6 by 3x-1.

$$5x+46\leq 18x-6$$

Subtract 18x from both sides.

$$5x+46-18x\leq -6$$

Combine 5x and -18x to get -13x.

$$-13x+46\leq -6$$

Subtract 46 from both sides.

$$-13x\leq -6-46$$

Subtract 46 from -6 to get -52.

$$-13x\leq -52$$

Divide both sides by -13. Since -13 is negative, the inequality direction is changed.

$$x\geq \frac{-52}{-13}$$

Divide -52 by -13 to get 4.

$$x\geq 4$$