Ten times the sum of a number 15 and is at least 21
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Let x = the number
"Ten times the sum of a number and 22 is at least 21" means
Ten times [the sum of a number and 22] is at least 21 means
10 * ( x + 22 ) ≥ 21
10(x+22) ≥ 21
10x + 220 ≥ 21 [distribute]
10x ≥ -199 [subtract 220 from both sides retains the sense of the inequality]
x ≥ -19.9 [divide both sides by 10 retains the sense of the inequality]
Check:
Use -20 [note: should be false]
Is 10(-20+22) ≥ 21 ?
10(2) ≥ 21 >
20 ≥ 21 ?no
Use 0 [note: should be true]
Is 10(0 + 22) ≥ 21 ?
220 ≥ 21 ?yes
Three times the sum of a number and 21 is less than 20
Let's solve this step-by-step:
Step 1: Let's define the unknown number. Let's call it "x".
Step 2: The expression "ten times the sum of a number 15" can be written as 10(15). So, we have 10(15).
Step 3: We are given that this expression is at least 21. So, we have the inequality 10(15) ≥ 21.
Step 4: Simplifying the left side of the inequality gives us 150 ≥ 21.
Step 5: Now we can solve for x. Since 150 is greater than 21, this inequality is true for any value of x.
Therefore, the solution to the inequality "ten times the sum of a number 15 is at least 21" is x can be any real number.
To find the number, we need to solve the inequality that represents the statement "Ten times the sum of a number 15 is at least 21."
Let's break it down step by step:
Step 1: Define the unknown number
Let's call the unknown number "x".
Step 2: Determine the sum of the number 15
The sum of the number 15 is x + 15.
Step 3: Multiply the sum by 10
Ten times the sum of the number 15 is written as 10 * (x + 15).
Step 4: Set up the inequality
The statement "Ten times the sum of a number 15 is at least 21" can be written as:
10 * (x + 15) ≥ 21
Step 5: Solve the inequality
To solve the inequality, we isolate the variable x. Let's go through the steps:
10 * (x + 15) ≥ 21
Divide both sides by 10:
x + 15 ≥ 21
Subtract 15 from both sides:
x ≥ 21 - 15
x ≥ 6
So the value of the unknown number is x ≥ 6. This means that any value of x greater than or equal to 6 will satisfy the given inequality.