Question

What is the value of x in the equation StartFraction 4 Over 7 EndFraction (StartFraction 21 Over 8 EndFraction x + one-half) = negative 2 (StartFraction 1 Over 7 EndFraction minus StartFraction 5 Over 28 EndFraction x)? Write your solution in decimal form.

Answer 1

X = -0.5

Explanation:

Edge 2020

Answer 2

x = -0.5

Explanation:

`(4)/(7)\left((21)/(8)x+(1)/(2)\right)=-2\left((1)/(7)-(5)/(28)x\right)\\\\\text{use the distributive property}\ a(b\pm c)=ab\pm ac\\\\\left((4)/(7)\right)\left((21)/(8)x\right)+\left((4)/(7)\right)\left((1)/(2)\right)=(-2)\left((1)/(7)\right)-(-2)\left((5)/(28)x\right)\\\\(4\cdot21)/(7\cdot8)x+(4\cdot1)/(7\cdot2)=-(2)/(7)+(2\cdot5)/(28)x\qquad\text{simplify}`

`(3)/(2)x+(2)/(7)=-(2)/(7)+(5)/(14)x\qquad\text{multiply both sides by 14}\\\\(14)\left((3)/(2)x\right)+(14)\left((2)/(7)\right)=(14)\left(-(2)/(7)\right)+(14)\left((5)/(14)x\right)\qquad\text{simplify}\\\\(7)(3x)+(2)(2)=(2)(-2)+(1)(5x)\\\\21x+4=-4+5x\qquad\text{subtract 4 from both sides}\\\\21x+4-4=-4-4+5x\\\\21x=-8+5x\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\21x-5x=-8+5x-5x\\\\16x=-8\qquad\text{divide both sides by 16}`

`(16x)/(16)=(-8)/(16)\qquad\text{simplify}\\\\\boxed{x=-(1)/(2)\to x=-0.5}`