Question 370·Medium·Algebra

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A number $x$ is at least $4$ more than twice the value of $y$ . If $y = 5$ , what is the least possible value of $x$ ?

Your answer

The phrase at least signals an inequality: it gives a range of values, not one fixed value. Build the amount being compared with $x$ , then substitute the given value of $y$ . Graph the inequality in Desmos and use its included lower boundary for the least value. Be careful not to turn “4 more” into subtraction.

Hints

Hint 1
Build the expression first: twice $y$ gives $2y$ , and 4 more adds $4$ to that result. If $x$ is at least that amount, which way should the inequality sign point?
Hint 2
An inclusive inequality allows equality. At least means $x$ can equal the amount you calculated. After replacing $y$ with $5$ , look for the first value of $x$ that the inequality allows.

Step-by-step

Graph the lower bound
Step 1
Translate the comparison
Twice $y$ is $2y$ , and 4 more makes $2y+4$ . “At least” means $x$ can equal that amount or be greater, so write the inequality:
$x\ge 2y+4.$
Step 2
Find the least allowed value
Put the given $5$ in for $y$ :
$x\ge 2(5)+4.$
Type $x\ge 2(5)+4$ in Desmos. It shades to the right of the solid boundary at $x=14$ . The line is solid because at least includes equality. For a least value, use the included lower boundary. So the least possible value of $x$ is $14$ . Grid in 14.

Question 370·Medium·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

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Strategy

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