2.2 Evaluate, simplify, and translate expressions

Solution

ⓐ To evaluate, substitute $3$ for $x$ in the expression, and then simplify.

Given.
Substitute.
Add.

When $x=3,$ the expression $x+7$ has a value of $10.$

ⓑ To evaluate, substitute $12$ for $x$ in the expression, and then simplify.

Given.
Substitute.
Add.

When $x=12,$ the expression $x+7$ has a value of $19.$

Notice that we got different results for parts ⓐ and ⓑ even though we started with the same expression. This is because the values used for $x$ were different. When we evaluate an expression, the value varies depending on the value used for the variable.

Solution

Remember $ab$ means $a$ times $b,$ so $9x$ means $9$ times $x.$

ⓐ To evaluate the expression when $x=5,$ we substitute $5$ for $x,$ and then simplify.

Multiply.
Subtract.

ⓑ To evaluate the expression when $x=1,$ we substitute $1$ for $x,$ and then simplify.

Multiply.
Subtract.

Notice that in part ⓐ that we wrote $9\cdot 5$ and in part ⓑ we wrote $9(1).$ Both the dot and the parentheses tell us to multiply.

Solution

We substitute $10$ for $x,$ and then simplify the expression.

Use the definition of exponent.
Multiply.

When $x=10,$ the expression $x^2$ has a value of $100.$

Solution

In this expression, the variable is an exponent.

Use the definition of exponent.
Multiply.

When $x=5,$ the expression $2^x$ has a value of $32.$

Solution

This expression contains two variables, so we must make two substitutions.

Multiply.
Add and subtract left to right.

When $x=10$ and $y=2,$ the expression $3x+4y-6$ has a value of $32.$

Solution

We need to be careful when an expression has a variable with an exponent. In this expression, $2x^2$ means $2\cdot x\cdot x$ and is different from the expression ${(2x)}^2,$ which means $2x\cdot 2x.$

Simplify $4^2$ .
Multiply.
Add.