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# 7x + 10 = 5x - 3

Hi Joana,

To solve this problem, remember that what you do on one side must be done on the other side. This ensures that you don't change the original equation given. (I will be happy to elaborate if that is unclear).

The goal is to isolate x. To do this, you want all of the terms with x's on one side:

7x + 10 = 5x - 3
-5x______-5x            Subtract 5x from both sides (5x-5x=0)
2x + 10 = -3

Next, you want all of the constants on the other side. This helps further isolate x:

2x + 10 = -3
-10     -10       Subtract 10 from both sides (10-10=0)
2x = -13

Finally, you want to eliminate all of the coefficients on x. These numbers are being multiplied by x, not added. Therefore, you must divide them on both sides:

2x = -13
2       2       Divide 2 on both sides (2x/2 = x)
x=-13/2 or -6.5

Hope this helps! Please let me know if you have any further questions.

7x+10=5x-3, Solution x=-13/2 or x= -5 3/2

Step by step Solution: step 1: re agruping similar terms

(a)sdd -5x the whole equation

-5x+7x+10=-5x+5x-3 ==>2x+10=-3

(b) add -10 the whole equation

2x+10=-3 ==> -10+2x+10=-10-3 ==> 2x=-13

step 2: mult by 1/2 the whole equation

2x=-13 ==> (1/2)2x=(1/2)*-13 ==> x=-13/2 0r x=-5 3/2 ========================================================================= Proof: 7x+10=5x-3, Does x=-13/2 or x= -5 3/2 is the solution of 7x+10=5x-3?

7x+10=5x-3,x= -13/2 substituing this value:

7*-13/2+10=?=5*-13/2-3 ==> -91/2+20/2=?=-65/2-6/2 ==> -71/2=-71/2

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