Question

What numbers should go in the boxes to complete the calculation

below?
2(-5x)+(4x-1)=2(3x+4)

Answer 1

2(6-5x) + 4(4x-1) = 2(3x+4)

First, expand the bracket on the right.

2(3x + 4)

6x + 8

Next, rewrite the equation.

2( -5x)+ (4x-1) = 6x + 8

expand what you can:

-10x

at the moment, only -10x comes out of this. however, you know that the other number added to -10x must make it equal 6x. so, the other number must be 16x:

-10x + 16x = 6x

so, 4 times 4x equal 16x. this is the second missing number:

4(4x-1) = 16x -4

with this new information you can see that:

-10x (+-)? + 16x -4 = 6x + 8

12 + (-4) = 8

and 2 times 6 = 12

so:

2(6-5x) + 4(4x-1) = 2(3x+4)

this is much easier on pen and paper trust me. and easier to explain.

sorry if its hard to understand i skipped some working but you should be able to get the general gist of it. feel free to ask if you have any questions or if you think i went wrong somewhere. always looking to improve

Answer 2

The number to go in the box are 6,4. The resulting equation is 2(6 -5x) +4(4x -1) = 2(3x +4).

You want to know the values of 'a' and 'b' that make the equation true:

2(a -5x) +b(4x -1) = 2(3x +4)

Simplify

Simplifying the equation gives us ...

2a -10x +4bx -b = 6x +8

(-10 +4b)x +(2a -b) = 6x +8

Matching coefficients

Making the coefficients of x match, we have ...

-10 +4b = 6

4b = 16 . . . . . . . add 10

b = 4 . . . . . . . . . divide by 4

Making the constants match, we have ...

2a -b = 8

2a = 8 +4 . . . . add b and substitute its value

a = 6 . . . . . . . . divide by 2

The numbers 6 and 4 go in the first and second boxes, respectively. The resulting equation is 2(6 -5x) +4(4x -1) = 2(3x +4)