Presentation on theme: "4 step by step on solving linear equations"— Presentation transcript:
1 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.
2 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-cMultiplication 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/cGoal 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.
3 STEP BY STEP ……. Ex 1) 3/7x+9=15 Solution Your goal is to isolate the variable on one side of the equation1st step: /7x+9= write original equation2nd 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= simplifyChecking : check x = 14 in the original equation.3/7(14)+9= substitute 14 for x15 = solution checks
4 Step by step 2… Solving an equation with a variable on both sides. Solve 5n+11=7n write original equation11=2n subtract 5n from each side.20=2n add 9 to each side10=n divide each side by 2.The solution is 10. check this in the original equation.
5 Step by step 3 Using the distributive property Solve 4(3x-5)=-2(-x+8)-6x4(3x-5)=-2(-x+8)-6x write original equation12x-20=2x-16-6x distributive property12x-20=-4x combine like terms.16x-20= add 4x to each side16x= add 20 to each sideX=1/4 divide each side by 16The solution is 1/4 . Check this in the original equation.
6 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 solution12(1/3x+1/4)=12(x-1/6) multiply each side by the LCD, 124x+3=12x distributive property3=8x subtract 4x from each side5 = 8x add 2 to each side5/8 =x divide each side by 8The solution is 5/8. check this in the original equation.