Solve 1.4(z+0.5)=0.7(z-13)

$$1.4 ( z + 0.5 ) = 0.7 ( z - 13 )$$

Solve for z

$$z=-14$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1.4 by z+0.5.

$$1.4z+0.7=0.7\left(z-13\right)$$

Use the distributive property to multiply 0.7 by z-13.

$$1.4z+0.7=0.7z-9.1$$

Subtract 0.7z from both sides.

$$1.4z+0.7-0.7z=-9.1$$

Combine 1.4z and -0.7z to get 0.7z.

$$0.7z+0.7=-9.1$$

Subtract 0.7 from both sides.

$$0.7z=-9.1-0.7$$

Subtract 0.7 from -9.1 to get -9.8.

$$0.7z=-9.8$$

Divide both sides by 0.7.

$$z=\frac{-9.8}{0.7}$$

Expand \frac{-9.8}{0.7} by multiplying both numerator and the denominator by 10.

$$z=\frac{-98}{7}$$

Divide -98 by 7 to get -14.

$$z=-14$$