If [tex]$p=2, q=-\frac{3}{2}$[/tex], and [tex]$r=-2$[/tex], evaluate [tex]$p q-r+1$[/tex].
Answer (2)
To evaluate pq − r + 1 with the given values, we substitute and calculate to find that the answer is 0 . After substituting and simplifying, we arrive at the conclusion that the expression evaluates to zero. This demonstrates basic algebraic manipulation skills systematically.
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Substitute the given values p = 2 , q = − 2 3 , and r = − 2 into the expression pq − r + 1 .
Calculate the product pq = 2 × ( − 2 3 ) = − 3 .
Substitute the result into the expression: − 3 − ( − 2 ) + 1 = − 3 + 2 + 1 .
Simplify the expression to obtain the final result: − 3 + 2 + 1 = 0 . The final answer is 0 .
Explanation
Understanding the Problem We are given the values p = 2 , q = − 2 3 , and r = − 2 . We need to evaluate the expression pq − r + 1 .
Substituting the Values First, we substitute the given values into the expression: pq - r + 1 = (2)\left(-\frac{3}{2}\\right) - (-2) + 1
Calculating the Product Next, we perform the multiplication: ( 2 ) ( − 2 3 ) = − 3
Substituting the Result Now, we substitute this result back into the expression: − 3 − ( − 2 ) + 1 = − 3 + 2 + 1
Simplifying the Expression Finally, we simplify the expression: − 3 + 2 + 1 = − 1 + 1 = 0
Final Answer Therefore, the value of the expression pq − r + 1 is 0.
Examples
Understanding how to substitute values into algebraic expressions is a fundamental skill in mathematics. In real life, this skill is used in various fields such as physics, engineering, and economics. For example, in physics, you might use a formula to calculate the force acting on an object, where you need to substitute the values of mass and acceleration. Similarly, in economics, you might use a formula to calculate the profit of a business, where you need to substitute the values of revenue and cost. Mastering this skill will help you solve many practical problems.
