Question

Solve the linear equation. 8x+32=2(25x−15)−11x8x+32=2(25x−15)−11x

Answer 1

It seems like you put the same equation up there twice, but no worries! :)

8x + 32 = 2(25x - 15) - 11x

Simplify.

8x + 32 = 50x - 30 - 11x

Add like terms.

8x + 32 = (50x - 11x) - 30

Simplify.

8x + 32 = 39x - 30

Now we must subtract 32 from both sides.

8x = 39x - 30 - 32

Then, subtract 39x from both sides.

8x - 39x = -30 - 32

Simplify.

-31x = -62

Finally, divide both sides by -31.

-31x ÷ -31 = -62 ÷ -31

Simplify.

x = 2

~Hope I helped!~

Answer 2

Part I: Simplifying the L.H.S and the R.H.S

Given equation:

• $8x + 32 = 2(25x - 15) - 11x$

Left hand side of the linear equation: $8x + 32$

The left-hand side has been simplified. This cannot be simplified further. Let us take a look on the right-hand side of the linear equation.

Right hand side of the linear equation: $2(25x - 15) - 11x$

On this side of the equation, we can see that a distributive property is included. To simplify the distributive property, we can multiply the term outside the parentheses with all the terms inside the parentheses.

        $\implies 2(25x - 15) - 11x$

        $\implies 50x - 30 - 11x$

Now, we can combine like terms to simplify the expression.

        $\implies 50x - 30 - 11x$

        $\implies x(50 - 11) - 30$

        $\implies x(39) - 30$

        $\implies39x - 30$

Part II: Solving for the value of x:

        $\implies 8x + 32 = 2(25x - 15) - 11x$

Now, substitute the simplified expressions for the L.H.S and the R.H.S

        $\implies 8x + 32 = 2(25x - 15) - 11x$

        $\implies 8x + 32 = 39x - 30$                 [L.H.S = 8x + 32; R.H.S = 39x - 30]

Finally, isolate the x-variable to determine its value.

        $\implies 8x - 8x + 32 = 39x - 30 - 8x$          (Subtracting 8x on both sides)

        $\implies32 = 31x - 30$                                       (Simplifying both sides)

        $\implies32 + 30 = 31x - 30 + 30$                    (Adding 30 on both sides)

        $\implies62 = 31x$                                              (Simplifying both sides)

        $\implies \dfrac{62}{31} = \dfrac{31x}{31}$                                          (Dividing 31 on both sides)

        $\implies \boxed{x = 2}$                                                (Simplifying both sides)

Therefore, the value of x is 2.

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