Question

1.) 6x - 7 - 3x = 6x + -7 + -3x = 6x + -3x + -7
2.) 4z - 10 - 9z =
3.) -6c - 4 - 5c =
4.) 2x - 3y - 5x + 8y =
5.) 4a + 2b - 6a - 5b =
6.) -5x - (-2) + 2x + 8 =
7.) 11x - 3 - (-2x) - 4 =
8.) -3x - 7 - x - 8 =
9.) 7x - x - (-2x) =
10.) -4y - 2b + 4y - 2b =

Explanation:

Step1: Simplify \(4z - 10 - 9z\)

Combine like terms (the \(z\)-terms). \(4z-9z=-5z\), so the expression becomes \(-5z - 10\).

Step2: Simplify \(-6c - 4 - 5c\)

Combine the \(c\)-terms: \(-6c-5c = -11c\), so we have \(-11c - 4\).

Step3: Simplify \(2x - 3y - 5x + 8y\)

Combine \(x\)-terms: \(2x-5x=-3x\), and \(y\)-terms: \(-3y + 8y = 5y\). Result: \(-3x + 5y\).

Step4: Simplify \(4a + 2b - 6a - 5b\)

Combine \(a\)-terms: \(4a-6a=-2a\), and \(b\)-terms: \(2b-5b=-3b\). Result: \(-2a - 3b\).

Step5: Simplify \(-5x - (-2) + 2x + 8\)

Simplify the double negative: \(-(-2)=2\). Combine \(x\)-terms: \(-5x + 2x=-3x\), and constants: \(2 + 8 = 10\). Result: \(-3x + 10\).

Step6: Simplify \(11x - 3 - (-2x) - 4\)

Simplify the double negative: \(-(-2x)=2x\). Combine \(x\)-terms: \(11x+2x = 13x\), and constants: \(-3-4=-7\). Result: \(13x - 7\).

Step7: Simplify \(-3x - 7 - x - 8\)

Combine \(x\)-terms: \(-3x - x=-4x\), and constants: \(-7-8=-15\). Result: \(-4x - 15\).

Step8: Simplify \(7x - x - (-2x)\)

Simplify the double negative: \(-(-2x)=2x\). Combine \(x\)-terms: \(7x - x+2x = 8x\). Result: \(8x\).

Step9: Simplify \(-4y - 2b + 4y - 2b\)

Combine \(y\)-terms: \(-4y + 4y = 0\), and \(b\)-terms: \(-2b-2b=-4b\). Result: \(-4b\).

(Note: For the first problem \(6x - 7 - 3x\), combine \(x\)-terms: \(6x-3x = 3x\), so result is \(3x - 7\))

Answer:

s (for each problem in order):

1. \(3x - 7\)
2. \(-5z - 10\)
3. \(-11c - 4\)
4. \(-3x + 5y\)
5. \(-2a - 3b\)
6. \(-3x + 10\)
7. \(13x - 7\)
8. \(-4x - 15\)
9. \(8x\)
10. \(-4b\)