Solve 1.6x-4-5+x<1-2/3x

$$1.6x-4-5+x < 1- \frac{ 2 }{ 3 } x$$

Solve for x

$$x<\frac{150}{49}$$

Solution Steps

Subtract 5 from -4 to get -9.

$$1.6x-9+x<1-\frac{2}{3}x$$

Combine 1.6x and x to get 2.6x.

$$2.6x-9<1-\frac{2}{3}x$$

Add \frac{2}{3}x to both sides.

$$2.6x-9+\frac{2}{3}x<1$$

Combine 2.6x and \frac{2}{3}x to get \frac{49}{15}x.

$$\frac{49}{15}x-9<1$$

Add 9 to both sides.

$$\frac{49}{15}x<1+9$$

Add 1 and 9 to get 10.

$$\frac{49}{15}x<10$$

Multiply both sides by \frac{15}{49}, the reciprocal of \frac{49}{15}. Since \frac{49}{15} is positive, the inequality direction remains the same.

$$x<10\times \frac{15}{49}$$

Express 10\times \frac{15}{49} as a single fraction.

$$x<\frac{10\times 15}{49}$$

Multiply 10 and 15 to get 150.

$$x<\frac{150}{49}$$