Solve the following equation for x: 4-5(x-2) = -9x + 7
and
x/5 = 4 + x/7
2006-10-22 16:05:32 · 7 answers · asked by lostinmath 1 in Science & Mathematics ➔ Mathematics
4 - 5(x - 2) = -9x + 7
Distribute the 5:
4 - 5x + 10 = -9x + 7
Collect terms:
4x = -7
Divide both sides by 4:
x = -7/4
x/5 = 4 + x/7
Collect terms:
x/5 - x/7 = 4
Find LCD of left side (35):
(7x - 5x) / 35 = 4
(2/35)x = 4
Multiply both sides by 35/2:
x = 140/2 = 70
2006-10-22 16:11:43 · answer #1 · answered by Anonymous · 0⤊ 0⤋
the trick is to first expand and then get all the x part on the left hand side(LHS) of the equation and numericals on the right hand side(RHS) and simplify
4-5(x-2) = -9x + 7
expand first
4-5x+10 = -9x + 7
now let us get x parts on LHS and mumeicals on RHS
-5x+9x = 7-4-10
simplify
4x =-7
so x = -7/4
x/5 = 4+x/7
get x part on LHS
x/5-x/7 = 4
getrid of fractions
LCD is 5*7= 35
mutilpy both sides by 35
7x-5x = 4*35 =140
simplify
2x = 140
so x = 70
Check
substitute for x as 70 in the equation x/5 = 4+x/7
LHS is 70/5 =14 =14
RHS is 4+70/7 = 4+10 = 14
since LHS= RHS the answer x = 70 is correct
2006-10-22 22:27:11 · answer #2 · answered by grandpa 4 · 0⤊ 0⤋
1) 4 - 5(x-2) = -9x + 7
9x - 5x + 10 = 7 -4
4x +10 = 3
4x = -10 + 3
x = -7/4
2)
x/5 = 4 + x/7
x = 20 + 5x/7
7x = 20 * 7 + 5x
7x - 5x = 140
2x = 140
x = 140/2
x = 70
2006-10-22 16:11:35 · answer #3 · answered by nanduri p 2 · 0⤊ 0⤋
4-5(x-2) = -9x + 7 : simplify by multiplying through
4 - 5x + 10 = -9x + 7 : add like terms
14 - 5x = 7 - 9x : combine terms
(14 - 5x ) + 5x -7 = ( 7 - 9x ) + 5x -7
14 -7 - 5x + 5x = 7 - 7 -9x + 5x
7 = -4x
-7/4 = x
--------------------
x/5 = 4 + x/7 : multiply by 35 to clear out the fractions
35(x/5) = 35(4 + x/7) : simplify by multiplying through
7x = 140 + 5x :combine terms
2x = 140 : simplify
x = 70
2006-10-22 16:16:32 · answer #4 · answered by RichardPaulHall 4 · 0⤊ 0⤋
Always get the terms collected.
for x/5 = 4 + x/7, multiply by 35 on both sides, to get rid of the fractions
so 7x = 140 +5x
2x = 140
x=70
2006-10-22 16:10:59 · answer #5 · answered by John T 6 · 0⤊ 0⤋
4-5(x-2) = -9x + 7
First, multiply through (x-2) by -5:
4 - 5x -5(-2) = -9x + 7
4 - 5x + 10 = -9x + 7, regroup:
-5x + 10 + 4 = -9x + 7, add like terms,
-5x + 14 = -9x + 7, add 9x - 14 to both sides:
+9x - 14 = +9x -14
4x..........=.........-7, divide both sides by 4
x/5 = 4 + x/7, Multiply both sides by 5:
x = 20 + 5x/7, Multiply again by 7:
+7x = 140 + 5x, Subtract 5x from both sides:
-5x = ........-5x
2x = 140, Divide both sides by 2.
2006-10-22 16:28:29 · answer #6 · answered by Helmut 7 · 0⤊ 0⤋
4-5x+10=-9x+7
4x=-14+7
x=-7/4
7x=5(28+x)
2x=140
x=70
2006-10-22 16:17:01 · answer #7 · answered by smart-crazy 4 · 0⤊ 0⤋