Solve 3-x/4-x+4/5=1-5x+7/2

$$\frac{ 3-x }{ 4 } - \frac{ x+4 }{ 5 } =1- \frac{ 5x+7 }{ 2 }$$

Solve for x

$$x = -\frac{49}{41} = -1\frac{8}{41} \approx -1.195121951$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 20, the least common multiple of 4,5,2.

$$5\left(3-x\right)-4\left(x+4\right)=20-10\left(5x+7\right)$$

Use the distributive property to multiply 5 by 3-x.

$$15-5x-4\left(x+4\right)=20-10\left(5x+7\right)$$

Use the distributive property to multiply -4 by x+4.

$$15-5x-4x-16=20-10\left(5x+7\right)$$

Combine -5x and -4x to get -9x.

$$15-9x-16=20-10\left(5x+7\right)$$

Subtract 16 from 15 to get -1.

$$-1-9x=20-10\left(5x+7\right)$$

Use the distributive property to multiply -10 by 5x+7.

$$-1-9x=20-50x-70$$

Subtract 70 from 20 to get -50.

$$-1-9x=-50-50x$$

Add 50x to both sides.

$$-1-9x+50x=-50$$

Combine -9x and 50x to get 41x.

$$-1+41x=-50$$

Add 1 to both sides.

$$41x=-50+1$$

Add -50 and 1 to get -49.

$$41x=-49$$

Divide both sides by 41.

$$x=\frac{-49}{41}$$

Fraction \frac{-49}{41} can be rewritten as -\frac{49}{41} by extracting the negative sign.

$$x=-\frac{49}{41}$$