Equation Word Problems 4
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Question 1 of 5
1. Question
Half of `x` plus `8` is equal to half the sum of `3x` and `-2`. Solve for `x`.- `x=` (9)
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Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.Keywords for Word Problems Keyword Meaning Certain number Unknown variable (`x,y,z,` etc) is the same as, The answer is, is equal `=` sum, and, plus, more than `+` subtracted, less, minus `-` times, product, multiplied, twice `times` half of, divide by `divide` First, form an equation using the information given.Half of `x` plus `8` is equal to half the sum of `3x` and `-2` `x/2` `+` `8` `=` `1/2` `(3x-2)` To solve for `x`, it needs to be alone on one side.Remove `1/2` by multiplying both sides of the equation by `2`.$$\frac{\color{#00880A}{x}}{2}+8$$ `=` `1/2(3``x` `-2)` $$\left(\frac{\color{#00880A}{x}}{2}+8\right)\color{#CC0000}{\times2}$$ `=` `1/2(3``x` `-2)``times2` `x` `+16` `=` `3``x` `-2` `1/2times2` cancels out Move `x` to the other side by subtracting `x` from both sides of the equation.`x` `+16` `=` `3``x` `-2` `x` `+16` `-x` `=` `3``x` `-2` `-x` `16` `=` `2``x` `-2` `x-x` cancels out Next, move `2` to the other side by adding `2` to both sides of the equation.`16` `=` `2``x` `-2` `16` `+2` `=` `2``x` `-2` `+2` `18` `=` `2``x` `-2+2` cancels out Finally, remove `2` by dividing both sides of the equation by `2`.`18` `=` `2``x` `18``divide2` `=` `2``x``divide2` `9` `=` `x` `2divide2` cancels out `x` `=` `9` `x=9` -
Question 2 of 5
2. Question
`5` more than twice a number is the same as `3` times that number. What is the number?- (5)
Hint
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Well Done!
Incorrect
Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.Keywords for Word Problems Keyword Meaning Certain number Unknown variable (`x,y,z,` etc) is the same as, The answer is, is equal `=` sum, and, plus, more than `+` subtracted, less, minus `-` times, product, multiplied, twice `times` half of, divide by `divide` First, label the values and form an equation using the information given.Number`=x``5` more than twice a number is the same as `3` times that number `2x+5` `=` `3` `times` `x` Simplify the equation:`2x+5` `=` `3timesx` `2x+5` `=` `3x` To solve for `x`, it needs to be alone on one side.Start by moving `2x` to the other side by subtracting `2x` from both sides of the equation.`2``x` `+5` `=` `3``x` `2``x` `+5` `-2x` `=` `3``x` `-2x` `5` `=` `x` `2x-2x` cancels out `x` `=` `5` The number is `5`.`5` -
Question 3 of 5
3. Question
The product of a number and `3` is subtracted from `80`. If the answer is `38`, what is the number?- (14)
Hint
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Excellent!
Incorrect
Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.Keywords for Word Problems Keyword Meaning Certain number Unknown variable (`x,y,z,` etc) is the same as, The answer is, is equal `=` sum, and, plus, more than `+` subtracted, less, minus `-` times, product, multiplied, twice `times` half of, divide by `divide` First, label the values and form an equation using the information given.Number`=n`The product of a number and `3` is subtracted from `80`. The answer is `38` `80-(ntimes3)` `=` `38` Simplify the equation:`80-(ntimes3)` `=` `38` `80-3n` `=` `38` To solve for `n`, it needs to be alone on one side.Start by moving `80` to the other side by subtracting `80` from both sides of the equation.`80-3``n` `=` `38` `80-3``n` `-80` `=` `38` `-80` `-3``n` `=` `-42` `80-80` cancels out Make both sides of the equation positive by multiplying `-1` to each side.`-3``n` `=` `-42` `-3``n``times-1` `=` `-42``times-1` `3``n` `=` `42` Finally, remove `3` by dividing both sides of the equation by `3`.`3``n` `=` `42` `3``n``divide3` `=` `42``divide3` `n` `=` `14` `3divide3` cancels out The number is `14`.Check our workTo confirm our answer, substitute `n=14` to the original equation.`80-3n` `=` `38` `80-3(14)` `=` `38` Substitute `n=14` `80-42` `=` `38` `38` `=` `38` Since the equation is true, the answer is correct.`14` -
Question 4 of 5
4. Question
What are `3` consecutive numbers that add up to `72?`-
`1`st number `=` (23)`2`nd number `=` (24)`3`rd number `=` (25)
Hint
Help VideoCorrect
Excellent!
Incorrect
Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.Keywords for Word Problems Keyword Meaning Certain number Unknown variable (`x,y,z,` etc) is the same as, The answer is, is equal `=` sum, and, plus, more than `+` subtracted, less, minus `-` times, product, multiplied, twice `times` half of, divide by `divide` First, label the values and form an equation using the information given.`1`st number`=x``2`nd number`=x+1` (since it comes after the `1`st number)`3`rd number`=x+2` (since it comes after the `2`nd number)The sum of three consecutive numbers is `72` `x+x+1+x+2` `=` `72` Simplify the equation:`x+x+1+x+2` `=` `72` `3x+3` `=` `72` To solve for `x`, it needs to be alone on one side.Start by moving `3` to the other side by subtracting `3` from both sides of the equation.`3``x` `+3` `=` `72` `3``x` `+3` `-3` `=` `72` `-3` `3``x` `=` `69` `3-3` cancels out Next, remove `3` by dividing both sides of the equation by `3`.`3``x` `=` `69` `3``x``divide3` `=` `69``divide3` `x` `=` `23` `3divide3` cancels out Substitute `x=23` to find each number.`1`st number `=` `x` `=` `23` `2`nd number `=` `x` `+1` `=` `23` `+1` `=` `24` `3`rd number `=` `x` `+2` `=` `23` `+2` `=` `25` Check our workTo confirm our answer, add the `3` numbers and check if the sum is `72`.`23+24+25` `=` `72` `72` `=` `72` Since the equation is true, the answer is correct.`1`st number `=23``2`nd number `=24``3`rd number `=25` -
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Question 5 of 5
5. Question
The sum of three consecutive odd numbers is `51`. Find the numbers.-
`1`st number `=` (15)`2`nd number `=` (17)`3`rd number `=` (19)
Hint
Help VideoCorrect
Exceptional!
Incorrect
Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.Keywords for Word Problems Keyword Meaning Certain number Unknown variable (`x,y,z,` etc) is the same as, The answer is, is equal `=` sum, and, plus, more than `+` subtracted, less, minus `-` times, product, multiplied, twice `times` half of, divide by `divide` First, label the values and form an equation using the information given.`1`st number`=x``2`nd number`=x+2` (since odd numbers are `2` values apart)`3`rd number`=x+4` (since odd numbers are `2` values apart)The sum of three consecutive odd numbers is `51` `x+x+2+x+4` `=` `51` Simplify the equation:`x+x+2+x+4` `=` `51` `3x+6` `=` `51` To solve for `x`, it needs to be alone on one side.Start by moving `6` to the other side by subtracting `6` from both sides of the equation.`3``x` `+6` `=` `51` `3``x` `+6` `-6` `=` `51` `-6` `3``x` `=` `45` `6-6` cancels out Next, remove `3` by dividing both sides of the equation by `3`.`3``x` `=` `45` `3``x``divide3` `=` `45``divide3` `x` `=` `15` `3divide3` cancels out Substitute `x=15` to find each number.`1`st number `=` `x` `=` `15` `2`nd number `=` `x` `+2` `=` `15` `+2` `=` `17` `3`rd number `=` `x` `+4` `=` `15` `+4` `=` `19` Check our workTo confirm our answer, add the `3` numbers and check if the sum is `72`.`15+17+19` `=` `51` `51` `=` `51` Since the equation is true, the answer is correct.`1`st number `=15``2`nd number `=17``3`rd number `=19` -
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