Question

building inequalities to solve real - world problems: tutorial
1.05x > 14,713.02
x > \frac{14713.02}{1.05} \text{ divide both sides by 1.05.}
x > 14,012.40

part e
what does the result from part d tell you about nancys situation?
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Explanation:

Assuming \( x \) represents Nancy's original amount (e.g., income, sales, etc.) before a 5% increase (since \( 1.05x \) implies a 5% increase, as \( 1 + 0.05=1.05 \)), the inequality \( x > 14,012.40 \) tells us that Nancy’s original amount (the value of \( x \)) must be greater than $14,012.40$ for the inequality \( 1.05x > 14,713.02 \) to hold. For example, if \( 1.05x \) was representing her income after a 5% raise, this result means her income before the raise needed to be more than $14,012.40$ to have an income after the raise ( \( 1.05x \)) greater than $14,713.02$.

Answer:

Nancy's original value (represented by \( x \)) must be greater than \$14,012.40 for the inequality LXI1 to be true. For example, if LXI2 is her pre - increase income (with a 5% increase giving LXI3), her pre - increase income needs to exceed \$14,012.40 for her post - increase income to be over \$14,713.02.