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**4 step by step on solving linear equations**

Make sure to do this on a separate sheet of paper before you click for the answers.

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**Things you need to know before we get in to the problem….**

Transformations that produce equivalent equations. Addition property of equality: add the same number to both sides: if a = b then a + c=b= c. Subtraction property of equality subtract the same number from both sides: if a=b then a –c = b-c Multiplication property of equality Multiply both sides by the same nonzero number: if a =b and c is not equal to 0, then ac=bc. Division property of equality divide both sides by the same nonzero number if a=b and c is not equal to 0 than a/c=b/c Goal 1: solving a linear equation. An equation is a statement in which two expressions are equal. A linear equation in one variable is an equation that can be written in the form ax=b where a and b are constants and a is not equal to 0.

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**STEP BY STEP ……. Ex 1) 3/7x+9=15 Solution**

Your goal is to isolate the variable on one side of the equation 1st step: /7x+9= write original equation 2nd step: /7x= subtract 9 from each side. 3rd step: x=7/3( Multiply each side by 7/3, the reciprocal of 3/7. 4th step: x= simplify Checking : check x = 14 in the original equation. 3/7(14)+9= substitute 14 for x 15 = solution checks

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**Step by step 2… Solving an equation with a variable on both sides.**

Solve 5n+11=7n write original equation 11=2n subtract 5n from each side. 20=2n add 9 to each side 10=n divide each side by 2. The solution is 10. check this in the original equation.

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**Step by step 3 Using the distributive property**

Solve 4(3x-5)=-2(-x+8)-6x 4(3x-5)=-2(-x+8)-6x write original equation 12x-20=2x-16-6x distributive property 12x-20=-4x combine like terms. 16x-20= add 4x to each side 16x= add 20 to each side X=1/4 divide each side by 16 The solution is 1/4 . Check this in the original equation.

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**Step by step 4 Solving an equation with fractions Solve 1/3x+1/4=x-1/6**

1/3x+1/4=x-1/ write the original solution 12(1/3x+1/4)=12(x-1/6) multiply each side by the LCD, 12 4x+3=12x distributive property 3=8x subtract 4x from each side 5 = 8x add 2 to each side 5/8 =x divide each side by 8 The solution is 5/8. check this in the original equation.

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