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Simplifying Algebraic Expressions Practice
Fifty original questions covering the complete simplifying algebraic expressions lesson, with explanations and SAT-focused strategy.
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Question 1
Explanation
Like terms have identical variable parts and exponents. Both \(4x\) and \(-7x\) contain \(x^1\).
Question 2
Explanation
The signed number multiplying \(x\) is \(-9\), so that is the coefficient.
Question 3
Explanation
Addition and subtraction separate the expression into \(3a\), \(-2b\), and \(7\): three terms.
Question 4
Explanation
The variable parts match, so add coefficients: \((5+2)x=7x\). Do not multiply exponents when adding terms.
Question 5
Explanation
Combine only the \(y\)-terms: \((8-3)y=5y\); the constant remains, giving \(5y+4\).
Question 6
Explanation
The constants combine to \(8\), while \(-3x\) is unlike them. The result is \(8-3x\).
Question 7
Explanation
Multiply every term inside by \(4\): \(4x+4(3)=4x+12\).
Question 8
Explanation
Distribute \(-2\) to both terms: \(-2a+10\). Negative times negative is positive.
Question 9
Explanation
Combine coefficients \(3-5=-2\), retaining the constant: \(-2m+7\).
Question 10
Explanation
Distribution multiplies both addends: \(2(x+y)=2x+2y\).
Question 11
Explanation
The minus sign distributes as \(-1\): \(9p-2p-3=7p-3\).
Question 12
Explanation
Distribute first: \(6x-3+x\). Then combine \(x\)-terms to get \(7x-3\).
Question 13
Explanation
Add the coefficients using denominator \(4\): \(\frac24+\frac34=\frac54\), so the result is \(\frac54x\).
Question 14
Explanation
The commutative property changes the order of addends without changing the sum.
Question 15
Explanation
The associative property changes grouping while preserving order.
Question 16
Explanation
Combine variable terms \(4x-2x=2x\) and constants \(3+8=11\), giving \(2x+11\).
Question 17
Explanation
Distribute: \(10y+5-3y\). Combine like terms to get \(7y+5\).
Question 18
Explanation
Distribute \(-3\): \(-6z-12+5z\). Combining gives \(-z-12\).
Question 19
Explanation
Distribute: \(2a-6-4a-4\). Combine to obtain \(-2a-10\).
Question 20
Explanation
The first, second, and fourth terms all have variable part \(x^2\). The term \(8x\) has exponent \(1\).
Question 21
Explanation
\(x\) and \(y\) are different variable parts, so the terms cannot combine by addition. The expression remains \(2x+3y\).
Question 22
Explanation
Combine \(x^2\)-terms and \(x\)-terms separately: \((7-3)x^2+(2+1)x=4x^2+3x\).
Question 23
Explanation
Multiply each term: \(\frac23\cdot9x=6x\) and \(\frac23\cdot(-6)=-4\).
Question 24
Explanation
\(5x-1\) has no grouping to distribute and no like terms to combine. Each other expression can be simplified further.
Question 25
Explanation
Inside: \(2x-(3-x)=2x-3+x=3x-3\). Then \(4-(3x-3)=4-3x+3=7-3x\).
Question 26
Explanation
Add like-term coefficients: \(0.5+1.2=1.7\). The constant remains, giving \(1.7x-0.7\).
Question 27
Explanation
Distribute: \(3x+6+2x-10\). Combine to get \(5x-4\).
Question 28
Explanation
Distribute the outside negative: \(-x-2+3x=2x-2\).
Question 29
Explanation
Add corresponding terms: \(2x+x=3x\) and \(3y-4y=-y\), yielding \(3x-y\).
Question 30
Explanation
Subtract the whole second expression: \(5m-2-(2m+7)=5m-2-2m-7=3m-9\).
Question 31
Explanation
Distribute: \(6x-6x+10\). The variable terms cancel, leaving the constant \(10\).
Question 32
Explanation
Use denominator \(12\): \(\frac34=\frac9{12}\) and \(\frac16=\frac2{12}\), so the difference is \(\frac7{12}x\).
Question 33
Explanation
Distribute: \(-\frac25\cdot10x=-4x\) and \(-\frac25\cdot-15=+6\).
Question 34
Explanation
The commutative property permits reordering while each term keeps its sign: \(3a-5a+2b+b\).
Question 35
Explanation
The associative property changes grouping but not order: \((x+2)+5=x+(2+5)\).
Question 36
Explanation
First \(2x+3x-12=5x-12\). The bracket is \(x-2x-1=-x-1\); subtracting it gives \(5x-12+x+1=6x-11\).
Question 37
Explanation
Distribute: \(8x-12-6x-10+7\). Combine to get \(2x-15\).
Question 38
Explanation
An exponent on grouped addition is not a distributive multiplier. Expanding gives \(x^2+6x+9\), so the middle term is missing.
Question 39
Explanation
Group by degree: \((5-3)x^2+(-2+7)x+(3-8)=2x^2+5x-5\).
Question 40
Explanation
Inside bracket, \(2x-x+4=x+4\). Then \(3x+12-2x-2=x+10\).
Question 41
Explanation
Combining gives \((4+k)x\). Set the coefficient equal to \(9\): \(4+k=9\), so \(k=5\).
Question 42
Explanation
Distribute: \(ax+2a+bx-b\). Combine the \(x\)-terms to get \((a+b)x+2a-b\).
Question 43
Explanation
Distribute: \(3x-1-x-3\), which combines to \(2x-4\).
Question 44
Explanation
Distributing and combining gives \(3x-6+x=4x-6\). Each other pair contains a distribution or like-term error.
Question 45
Explanation
Remove parentheses: \(2x-3-4+5x+1-x\). Combine to \(6x-6\).
Question 46
Explanation
Perimeter is \(2(2x+1)+2(x-3)=4x+2+2x-6=6x-4\).
Question 47
Explanation
Distribute: \(3x+4-(x-3)=3x+4-x+3=2x+7\).
Question 48
Explanation
Simplify: \(2(3x+c)-x=5x+2c\). The constant is \(2c\), so \(2c=10\) and \(c=5\).
Question 49
Explanation
Distribute choice B: \(4x-4-4x+4=0\). All variable and constant terms cancel.
Question 50
Explanation
Inside: \(x-(2-x)=2x-2\); then \(3(2x-2)-4x=2x-6\); finally \(2(2x-6)+5=4x-7\).
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- Question 1Identify like termsEasy
- Question 2Identify coefficientsEasy
- Question 3Identify termsEasy
- Question 4Combine like termsEasy
- Question 5Combine like termsEasy
- Question 6Combine constantsEasy
- Question 7Distributive propertyEasy
- Question 8Negative distributionEasy
- Question 9Combine signed termsEasy
- Question 10Equivalent expressionsEasy
- Question 11Subtract expressionsEasy
- Question 12Multi-step simplificationEasy
- Question 13Fractional coefficientsEasy
- Question 14Algebraic propertiesEasy
- Question 15Algebraic propertiesEasy
- Question 16Rearrange and combineMedium
- Question 17Multi-step simplificationMedium
- Question 18Negative distributionMedium
- Question 19Multiple distributionsMedium
- Question 20Identify unlike termsMedium
- Question 21Error analysisMedium
- Question 22Polynomial simplificationMedium
- Question 23Fractional distributionMedium
- Question 24Simplest formMedium
- Question 25Nested subtractionMedium
- Question 26Decimal coefficientsMedium
- Question 27Multiple distributionsMedium
- Question 28Negative groupingMedium
- Question 29Add expressionsMedium
- Question 30Subtract expressionsMedium
- Question 31CancellationMedium
- Question 32Fractional coefficientsMedium
- Question 33Negative fractional distributionMedium
- Question 34Commutative rearrangementMedium
- Question 35Associative propertyMedium
- Question 36Complex simplificationMedium
- Question 37Complex simplificationMedium
- Question 38Exponent misconceptionMedium
- Question 39Polynomial simplificationMedium
- Question 40Nested distributionMedium
- Question 41Missing coefficientHard
- Question 42Symbolic simplificationHard
- Question 43Decimal distributionHard
- Question 44Equivalent expressionsHard
- Question 45Multiple signed groupsHard
- Question 46Applied simplificationHard
- Question 47Fractional multi-step simplificationHard
- Question 48Parameter reasoningHard
- Question 49Identity recognitionHard
- Question 50Complex nested simplificationHard