I need help solving these equations: SOLVE for X . . . ax + b + a(x + b) = b, a(x + c) + b(x + d) - ax = e, 3x - (x + n) = m, SOLVE for P. . . P/6rn = 7/9nx, f + P/3 = P/8, 2P/m - r/s = Ps + q/ms
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1.5: Literal Equations <ul><li>Goals: </li></ul><ul><li>Solve equations for a specific variable </li></ul><ul><li>Evaluate equations for a specific variable </li></ul>
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Review What it means to solve equations: <ul><li>To solve an equation for x means to get x by itself on one side of the equation. </li></ul><ul><li>( x = _____ ) </li></ul><ul><li>To solve an equation for y means to get y by itself on one side of the equation. </li></ul><ul><li>( y = _____ ) </li></ul><ul><li>Therefore, to solve for any variable is to get it by itself on one side of the equation. </li></ul>
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What are Literal Equations? <ul><li>A literal equation is an equation with more than one variable. </li></ul>AREA BASE HEIGHT
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Rules to Solving Literal Equations Solving equations for a specific variable involve the same rules as solving an equation. <ul><li>Simplify each side of the equation, if needed, by distributing or combining like terms. </li></ul><ul><li>2. Move the variable being solved for to one side of the equation by using the opposite operation of addition or subtraction. </li></ul><ul><li>3. Isolate the variable being solved for by itself by applying the opposite operation to each side. </li></ul><ul><ul><li>a. First , use the opposite operation of addition or subtraction to move any other constants or variables to the other side. </li></ul></ul><ul><ul><li>b. Second , use the opposite operation of multiplication or division to eliminate the coefficient of the variable being solved for. </li></ul></ul>
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Example: Solve the following for y In other words, isolate the variable “ y ” by itself Undo the subtracting 5x by adding 5x to both sides. Undo the multiplying by 2, by dividing both sides by 2 Remember, all numbers on the other side get divided by 2. Since you have “ y = “, you have now solved for y
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Example: Solve the same equation for x In other words, isolate the variable “ x ” by itself Undo the positive 2y by subtracting 2y from both sides. Undo the multiplying by -5, by dividing both sides by -5 Remember, all numbers on the other side get divided by -5. Since you have “ x = “, you have now solved for x Move the negative to the numerator by changing all the signs.
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Formula Examples: <ul><li>Solving literal equations allows you to transform formulas (such as area, volume, perimeter, etc) so you can solve for any of the parts: </li></ul>Solve the following formula for “ r ”
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Formula Examples: <ul><li>Since “r” is being multiplied by both the “2” and “ ” you would divide by “ 2 ” </li></ul>Solve the following formula for “ r ”
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Formula Examples: <ul><li>Since the equation now reads: </li></ul><ul><li>“ r = “ </li></ul><ul><li>the equation is solved. </li></ul>Solve the following formula for “ r ”
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Solve the following formula, the perimeter of a rectangle for “ w ” In other words, isolate the variable “ w ” by itself Undo the positive “2 l ” by subtracting “2 l ” Undo the multiplication by dividing both sides by 2 Remember, all the numbers get divided by 2
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Examples: On Your Own 1) ; Solve for b 2) ; Solve for y 3) ; Solve for y
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Examples: On Your Own <ul><li>1) Solve for b: </li></ul><ul><li>A = ½bh </li></ul><ul><li>2) Solve for y: </li></ul><ul><li>3(x-4y) = 24 </li></ul><ul><li>3) Solve for y: </li></ul><ul><li>5xy + 2z = 10 </li></ul>
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Examples: On Your Own <ul><li>1) Solve for b: </li></ul><ul><li>A = ½bh </li></ul><ul><li>2) Solve for y: </li></ul><ul><li>3(x-4y) = 24 </li></ul><ul><li>3) Solve for y: </li></ul><ul><li>5xy + 2z = 10 </li></ul>
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Examples: On Your Own <ul><li>1) Solve for b: </li></ul><ul><li>A = ½bh </li></ul><ul><li>2) Solve for y: </li></ul><ul><li>3(x-4y) = 24 </li></ul><ul><li>3) Solve for y: </li></ul><ul><li>5xy + 2z = 10 </li></ul>
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