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Basic Math Examples
7z-82z-2=317z−82z−2=31
Step 1
Step 1.1
Factor 22 out of 2z-22z−2.
Step 1.1.1
Factor 22 out of 2z2z.
7z-82(z)-2=317z−82(z)−2=31
Step 1.1.2
Factor 22 out of -2−2.
7z-82(z)+2(-1)=317z−82(z)+2(−1)=31
Step 1.1.3
Factor 22 out of 2(z)+2(-1)2(z)+2(−1).
7z-82(z-1)=317z−82(z−1)=31
7z-82(z-1)=317z−82(z−1)=31
Step 1.2
Divide 33 by 11.
7z-82(z-1)=37z−82(z−1)=3
7z-82(z-1)=37z−82(z−1)=3
Step 2
Step 2.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
2(z-1),12(z−1),1
Step 2.2
The LCM of one and any expression is the expression.
2(z-1)2(z−1)
2(z-1)2(z−1)
Step 3
Step 3.1
Multiply each term in 7z-82(z-1)=37z−82(z−1)=3 by 2(z-1)2(z−1).
7z-82(z-1)(2(z-1))=3(2(z-1))7z−82(z−1)(2(z−1))=3(2(z−1))
Step 3.2
Simplify the left side.
Step 3.2.1
Rewrite using the commutative property of multiplication.
27z-82(z-1)(z-1)=3(2(z-1))27z−82(z−1)(z−1)=3(2(z−1))
Step 3.2.2
Cancel the common factor of 22.
Step 3.2.2.1
Cancel the common factor.
27z-82(z-1)(z-1)=3(2(z-1))
Step 3.2.2.2
Rewrite the expression.
7z-8z-1(z-1)=3(2(z-1))
7z-8z-1(z-1)=3(2(z-1))
Step 3.2.3
Cancel the common factor of z-1.
Step 3.2.3.1
Cancel the common factor.
7z-8z-1(z-1)=3(2(z-1))
Step 3.2.3.2
Rewrite the expression.
7z-8=3(2(z-1))
7z-8=3(2(z-1))
7z-8=3(2(z-1))
Step 3.3
Simplify the right side.
Step 3.3.1
Apply the distributive property.
7z-8=3(2z+2⋅-1)
Step 3.3.2
Multiply 2 by -1.
7z-8=3(2z-2)
Step 3.3.3
Apply the distributive property.
7z-8=3(2z)+3⋅-2
Step 3.3.4
Multiply.
Step 3.3.4.1
Multiply 2 by 3.
7z-8=6z+3⋅-2
Step 3.3.4.2
Multiply 3 by -2.
7z-8=6z-6
7z-8=6z-6
7z-8=6z-6
7z-8=6z-6
Step 4
Step 4.1
Move all terms containing z to the left side of the equation.
Step 4.1.1
Subtract 6z from both sides of the equation.
7z-8-6z=-6
Step 4.1.2
Subtract 6z from 7z.
z-8=-6
z-8=-6
Step 4.2
Move all terms not containing z to the right side of the equation.
Step 4.2.1
Add 8 to both sides of the equation.
z=-6+8
Step 4.2.2
Add -6 and 8.
z=2
z=2
z=2