Solve the system by substitution x=4y-7 2x+9y=-31
1 answer:
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Given
An algebraic expression is the difference between seven times a number and three times that number.
To find:
The algebraic expression.
Solution:
Let x be the unknown number.
Multiplication is used for times and subtraction is used for difference.
7 times of a number = 7x
3 times of that number = 3x
The difference between seven times a number and three times that number is
Therefore, the algebraic expression for the given statement is 7x-3x and its simplified form is 4x.
Step 1 :
simplify
Equation at the end of step 1 :
15 (((3 • (x2)) - 4x) - ——) - 3 x
Step 2 :
Equation at the end of step 2 :
15 ((3x2 - 4x) - ——) - 3 x
Step 3 :
Rewriting the whole as an Equivalent Fraction :
3.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using x as the denominator :
3x2 - 4x (3x2 - 4x) • x 3x2 - 4x = ———————— = —————————————— 1 x
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Step 4 :
Pulling out like terms :
4.1 Pull out like factors :
3x2 - 4x = x • (3x - 4)
Adding fractions that have a common denominator :
4.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
x • (3x-4) • x - (15) 3x3 - 4x2 - 15 ————————————————————— = —————————————— x x
Equation at the end of step 4 :
(3x3 - 4x2 - 15) ———————————————— - 3 x
Step 5 :
Rewriting the whole as an Equivalent Fraction :
5.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using x as the denominator :
3 3 • x 3 = — = ————— 1 x