Since you did not select any specific options (ExplainAnswer, TeachTopic, or GeneratePractice are all false), I will provide the solutions to the algebra problems visible in the worksheet. I have grouped them by type to make it easier to check your work.
Here are the step-by-step solutions for the key problems shown in the "Algebra Revision" sheets.
Part 1: Simplifying Expressions & Finding Coefficients
Problem 1: Simplify $3x + 7 - 2x$ and find the coefficient of $x$.
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Step 1: Group the $x$ terms: $3x - 2x = 1x$ (or just $x$).
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Step 2: Keep the constant term: $+ 7$.
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Result: $x + 7$.
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Coefficient: The number in front of $x$ is
1.
Problem 2: Calculate the value of $2a - 5$, when $a = 3$.
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Step 1: Substitute $3$ for $a$: $2(3) - 5$.
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Step 2: Multiply: $6 - 5$.
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Result: 1.
Problem 3: Simplify $4b + 3b - b$.
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Step 1: Add the positive $b$'s: $4b + 3b = 7b$.
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Step 2: Subtract $b$: $7b - 1b = 6b$.
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Result: $6b$.
Problem 4: Calculate the value of $\frac{y}{2} + 4$, when $y = 10$.
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Step 1: Substitute $10$ for $y$: $\frac{10}{2} + 4$.
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Step 2: Divide: $5 + 4$.
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Result: 9.
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Part 2: Solving Equations
Problem 5: Solve the equation $3x + 5 = 20$.
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Step 1: Subtract 5 from both sides: $3x = 15$.
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Step 2: Divide by 3: $x = \frac{15}{3}$.
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Result: $x = 5$.
Problem 6: Solve the equation $2(x - 3) = 10$.
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Step 1: Divide both sides by 2: $x - 3 = 5$.
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Step 2: Add 3 to both sides: $x = 5 + 3$.
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Result: $x = 8$.
Problem 7: Solve the equation $5x - 2 = 3x + 8$.
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Step 1: Move $x$ terms to one side (subtract $3x$): $2x - 2 = 8$.
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Step 2: Move constants to the other side (add 2): $2x = 10$.
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Step 3: Divide by 2: $x = 5$.
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Result: $x = 5$.
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Part 3: Substitution with Negative Numbers
Problem 8: Calculate the value of $3m - 2n$, when $m = -2$ and $n = 4$.
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Step 1: Substitute the values: $3(-2) - 2(4)$.
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Step 2: Multiply: $-6 - 8$.
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Step 3: Subtract: $-6 - 8 = -14$.
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Result: $-14$.
Problem 9: Calculate the value of $p^2 + 3$, when $p = -4$.
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Step 1: Substitute $-4$ for $p$: $(-4)^2 + 3$.
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Step 2: Square the negative number (negative times negative is positive): $16 + 3$.
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Result: 19.
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Part 4: Expanding Brackets
Problem 10: Expand and simplify $3(x + 4) + 2(x - 1)$.
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Step 1: Expand the first bracket: $3 \times x = 3x$, $3 \times 4 = 12 \rightarrow 3x + 12$.
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Step 2: Expand the second bracket: $2 \times x = 2x$, $2 \times -1 = -2 \rightarrow 2x - 2$.
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Step 3: Combine them: $3x + 12 + 2x - 2$.
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Step 4: Group like terms: $(3x + 2x) + (12 - 2)$.
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Result: $5x + 10$.
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Final Answer
Here are the concise answers for the problems solved above:
1.
$x + 7$ (Coefficient of $x$ is
1)
2.
1
3.
$6b$
4.
9
5.
$x = 5$
6.
$x = 8$
7.
$x = 5$
8.
$-14$
9.
19
10.
$5x + 10$
Parent Tip: Review the logic above to help your child master the concept of algebra coloring worksheet.
