Evaluating Expressions

Learn substitution, negative inputs and powers.

Lesson 2 of 32 parts Practice Flashcards

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Substitution

Objective: Explain substitution, apply the stated method, and check its conditions.

Evaluating an expression replaces each variable by its assigned value, then uses the order of operations. Substitution does not solve for an unknown. Repeated occurrences of the same variable receive the same stated value throughout the calculation. Use the assigned value consistently at every occurrence.

Formulas

$If x=c, ax+b=ac+b$

Worked examples

Try itEvaluate 6x+7 at x=7.Show answer

Step 1: Substitute 7 for x. Step 2: Multiply 6·7=42. Step 3: Add 7 to get 49.

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Substitution

Objective: Explain substitution, apply the stated method, and check its conditions.

Formulas

$If x=c, ax+b=ac+b$

Worked examples

Try itEvaluate 6x+7 at x=7.Show answer

Step 1: Substitute 7 for x. Step 2: Multiply 6·7=42. Step 3: Add 7 to get 49.

Negative Inputs and Powers

Objective: Explain negative inputs and powers, apply the stated method, and check its conditions.

When substituting a negative value into a power, enclose the value in parentheses. For real c, (−c)²=c², while −c² means the negative of c squared under the usual precedence convention. Parentheses preserve the intended input. The expressions (−c)² and −c² have different meanings.

Formulas

$(−c)²=c²$

Worked examples

Try itEvaluate x²+7 when x=−7.Show answer

Step 1: Use parentheses: (−7)²+7. Step 2: The square is 49. Step 3: The value is 56.

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