Question

practice draw circles, rectangles, and triangles to help you combine like terms and simplify each expression.

1. 3a + 5 - x + 7x - 2a
2. 2x - 5 + 3a - 5x + 10a
3. 7b - b - x + 5 - 2x - 7b
4. -6m + 3t + 4 - 4m - 2t
5. 2r + 3s - \frac{5}{2}r
6. 4 - p - 2x + 3p - 7x
7. 3k - 2x + 6k + 5
8. 3 + 2a - 7x + 2.5 + 5x
9. 4a + 3 - 2y - 5a - 7 + 4y
10. c - 3 + 2x - 6c + 4x

Explanation:

Step1: Identify like - terms

For the expression \(3a + 5−x + 7x−2a\), the like - terms with the variable \(a\) are \(3a\) and \(-2a\), and the like - terms with the variable \(x\) are \(-x\) and \(7x\), and the constant term is \(5\).

Step2: Combine like - terms

Combining the \(a\) terms: \(3a-2a=(3 - 2)a=a\). Combining the \(x\) terms: \(-x + 7x=(-1 + 7)x = 6x\).
The simplified expression is \(a+6x + 5\).

We will follow the same steps for all the expressions:

1. \(3a + 5−x + 7x−2a\)

• Combine \(a\) terms: \(3a-2a=a\)
• Combine \(x\) terms: \(-x + 7x = 6x\)
• # Answer: \(a+6x + 5\)

1. \(2x-5 + 3a-5x + 10a\)

• Combine \(a\) terms: \(3a+10a = 13a\)
• Combine \(x\) terms: \(2x-5x=-3x\)
• # Answer: \(13a-3x-5\)

1. \(7b - b−x + 5−2x−7b\)

• Combine \(b\) terms: \(7b - b-7b=-b\)
• Combine \(x\) terms: \(-x-2x=-3x\)
• # Answer: \(-b-3x + 5\)

1. \(-6m+3t + 4-4m-2t\)

• Combine \(m\) terms: \(-6m-4m=-10m\)
• Combine \(t\) terms: \(3t-2t=t\)
• # Answer: \(-10m+t + 4\)

1. \(2r+3s-\frac{5}{2}r\)

• Combine \(r\) terms: \(2r-\frac{5}{2}r=\frac{4r - 5r}{2}=-\frac{1}{2}r\)
• # Answer: \(-\frac{1}{2}r+3s\)

1. \(4 - p-2x+3p-7x\)

• Combine \(p\) terms: \(-p + 3p = 2p\)
• Combine \(x\) terms: \(-2x-7x=-9x\)
• # Answer: \(2p-9x + 4\)

1. \(3k-2x+6k + 5\)

• Combine \(k\) terms: \(3k+6k = 9k\)
• # Answer: \(9k-2x + 5\)

1. \(3 + 2a-7x+2.5+5x\)

• Combine \(x\) terms: \(-7x+5x=-2x\)
• Combine constant terms: \(3 + 2.5=5.5\)
• # Answer: \(2a-2x+5.5\)

1. \(4a+3-2y-5a-7 + 4y\)

• Combine \(a\) terms: \(4a-5a=-a\)
• Combine \(y\) terms: \(-2y + 4y = 2y\)
• Combine constant terms: \(3-7=-4\)
• # Answer: \(-a+2y-4\)

1. \(c-3+2x-6c+4x\)

• Combine \(c\) terms: \(c-6c=-5c\)
• Combine \(x\) terms: \(2x+4x = 6x\)
• # Answer: \(-5c+6x-3\)

Answer:

Step1: Identify like - terms

For the expression \(3a + 5−x + 7x−2a\), the like - terms with the variable \(a\) are \(3a\) and \(-2a\), and the like - terms with the variable \(x\) are \(-x\) and \(7x\), and the constant term is \(5\).

Step2: Combine like - terms

Combining the \(a\) terms: \(3a-2a=(3 - 2)a=a\). Combining the \(x\) terms: \(-x + 7x=(-1 + 7)x = 6x\).
The simplified expression is \(a+6x + 5\).

We will follow the same steps for all the expressions:

1. \(3a + 5−x + 7x−2a\)

• Combine \(a\) terms: \(3a-2a=a\)
• Combine \(x\) terms: \(-x + 7x = 6x\)
• # Answer: \(a+6x + 5\)

1. \(2x-5 + 3a-5x + 10a\)

• Combine \(a\) terms: \(3a+10a = 13a\)
• Combine \(x\) terms: \(2x-5x=-3x\)
• # Answer: \(13a-3x-5\)

1. \(7b - b−x + 5−2x−7b\)

• Combine \(b\) terms: \(7b - b-7b=-b\)
• Combine \(x\) terms: \(-x-2x=-3x\)
• # Answer: \(-b-3x + 5\)

1. \(-6m+3t + 4-4m-2t\)

• Combine \(m\) terms: \(-6m-4m=-10m\)
• Combine \(t\) terms: \(3t-2t=t\)
• # Answer: \(-10m+t + 4\)

1. \(2r+3s-\frac{5}{2}r\)

• Combine \(r\) terms: \(2r-\frac{5}{2}r=\frac{4r - 5r}{2}=-\frac{1}{2}r\)
• # Answer: \(-\frac{1}{2}r+3s\)

1. \(4 - p-2x+3p-7x\)

• Combine \(p\) terms: \(-p + 3p = 2p\)
• Combine \(x\) terms: \(-2x-7x=-9x\)
• # Answer: \(2p-9x + 4\)

1. \(3k-2x+6k + 5\)

• Combine \(k\) terms: \(3k+6k = 9k\)
• # Answer: \(9k-2x + 5\)

1. \(3 + 2a-7x+2.5+5x\)

• Combine \(x\) terms: \(-7x+5x=-2x\)
• Combine constant terms: \(3 + 2.5=5.5\)
• # Answer: \(2a-2x+5.5\)

1. \(4a+3-2y-5a-7 + 4y\)

• Combine \(a\) terms: \(4a-5a=-a\)
• Combine \(y\) terms: \(-2y + 4y = 2y\)
• Combine constant terms: \(3-7=-4\)
• # Answer: \(-a+2y-4\)

1. \(c-3+2x-6c+4x\)

• Combine \(c\) terms: \(c-6c=-5c\)
• Combine \(x\) terms: \(2x+4x = 6x\)
• # Answer: \(-5c+6x-3\)