Let’s solve each expression by combining like terms — that means adding or subtracting the numbers with variables (like r, z, k, etc.) together, and then adding or subtracting the plain numbers (constants) together.
We’ll go one by one:
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1. 2r + 1 + (-4r) + 7
Combine r terms: 2r + (-4r) = -2r
Combine constants: 1 + 7 = 8
→
-2r + 8
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2. 3z + 2 + (-5z) + 6
Combine z terms: 3z + (-5z) = -2z
Combine constants: 2 + 6 = 8
→
-2z + 8
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3. -3z - z
This is -3z + (-1z) = -4z
→
-4z
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4. -4y - 4 + (-3)
Only one y term: -4y
Constants: -4 + (-3) = -7
→
-4y - 7
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5. -2k + (-4k) + 5
k terms: -2k + (-4k) = -6k
Constant: +5
→
-6k + 5
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6. 4t + 2 + (-3t) + 6
t terms: 4t + (-3t) = 1t → just t
Constants: 2 + 6 = 8
→
t + 8
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7. 4z - (-3z)
Subtracting a negative is like adding: 4z + 3z = 7z
→
7z
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8. -2k - (-5) + 1
-(-5) becomes +5
So: -2k + 5 + 1 = -2k + 6
→
-2k + 6
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9. -4q - (-8q) + 10
-(-8q) becomes +8q
So: -4q + 8q = 4q
Plus 10 →
4q + 10
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10. -4h + 3 + (-2h) + 3
h terms: -4h + (-2h) = -6h
Constants: 3 + 3 = 6
→
-6h + 6
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Final Answer:
-2r + 8
-2z + 8
-4z
-4y - 7
-6k + 5
t + 8
7z
-2k + 6
4q + 10
-6h + 6
Parent Tip: Review the logic above to help your child master the concept of algebraic formula worksheet.
