Solving Equations - Algebra?

Hi! So we need to find z, and to do so we first need to combine all the z's, then combine all the numbers, then get z by itself on one side. First let's distribute the parentheses.

To do that, we take the number that is multiplied by the parentheses, and multiply that number with the numbers inside. For an example: 5(x + 1) multiplied would be 5x + 5. So let's do that with the equation by distributing all the parentheses: 8z + 8 - 5z + 20 = 4z - 4 Ok, now that we distributed the parentheses, we can add the z terms.

We can do that by simply adding (or subtracting) their coefficients. The coefficient of a number is what it is multiplied by (e.g. in 4x the four would be the coefficient). So with 4x - 2x, you would take the coefficients add subtract them: 4 - 2 = 2.

So 4x - 2x would be 2x. So with the equation 8z - 5z would be 3z: 3z + 8 + 20 = 4z - 4 Let's add the two numbers on the left side: 3z + 28 = 4z - 4 Now we need to get the other 4z over on the left side. We can move it, but we need to change its sign.

That's a really important rule: move a number over and you need to change its sign. For instance: 5 moved to the other side would be changed to -5. -3.65 would be changed to 3.65.

So let's move 4z over, changing it to -4z: 3z - 4z + 28 = -4 3z - 4z is -z: -z + 28 = -4 Let's move the 28 over: -z = -28 - 4.

8z + 8 - 5z +20 = 4z -4 8z - 5z - 4z = -4 - 20 - 8 -z = -32 z = 32 ANSWER Check your answer 8 ( 33) - 5 ( 28) = 4 ( 31) 264 -140 = 124 124 = 124.

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