2.4 Start Thinking. 2.4 Warm Up. 2.4 Cumulative Review Warm Up
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1 .4 Start Tikig We solvig equatios, steps are typically doe i te opposite order of te order of operatios. or example, you eed to udo subtractio before multiplicatio to solve 3x = 4. escribe oe istace i wic you must multiply or divide before udoig additio or subtractio. reate a example to illustrate..4 Warm Up State te mistake made i solvig te equatio. Rewrite te solutio so it is correct.. f 3 = 7 f 3 3 = 7 3 f = 40 4 m = m = m = 7. 8r = 4 8r 4 = 8 8 r = 4. = = = 8.4 umulative Review Warm Up Write tree differet agles i te diagram... G H 56 Geometry opyrigt ig Ideas Learig, LL
2 Name ate.4 Practice I xercises 3, solve te equatio. Justify eac step. x + =. 3 ( x + = 5 ( 6 x 8) = ( x + 6) I xercises 4 6, solve te equatio for te give variable. Justify eac step. 4. p = ; v v 5. V = πr ; 6. S = πrs + πr ; s I xercises 7 ad 8, ame te property of equality tat te statemet illustrates. 7. If x = y, te x = y. 8. If m = m ad m = 4, te m = 4. I xercises 9, use te property to copy ad complete te statemet. 9. dditio Property of quality: If m J = 30, te m J + m K =. 0. Reflexive Property of quality: GH =. istributive Property: If 3( x + 7) = 30, te + = 30.. Te formula for te surface area of a rectagular prism is give by te equatio = w + + w, were is te legt, w is te widt, ad is te eigt. Solve te formula for w ad justify eac step. Te fid te widt of te prism if te total surface area is 5 square ices, te legt is ices, ad te eigt is 4 ices. I te diagram, = 3 ad = 5. id te perimeter of te exago. Justify your aswer usig te properties of equality. w opyrigt ig Ideas Learig, LL Geometry 57
3 Name ate.4 Practice I xercises ad, solve te equatio. Justify eac step.. 3( x 4) + 3 = x. ( x 5) 3 x ( x + = + I xercises 3 ad 4, solve te equatio for te give variable. Justify eac step. = 4. I mr ; m = mv m; I xercises 5 ad 6, ame te properties of equality tat te statemet illustrates. 5. If x = y, te x 6 = y If m = m ad m = 4, te m + 0 = 5. I xercises 7 ad 8, use te property to copy ad complete te statemet. 7. Multiplicatio Property of quality: If m J = 30, te m J =. 8. Trasitive Property: If 3x + y = 7 ad 7 = 5x y, te. 9. Te formula for te volume V of a triagular prism is give by te equatio V = b were, b is te base of te triagle, is te eigt of te triagle, ad is te legt of te prism. Solve te formula for b. Justify eac step. Te fid te base of a prism wit a volume of 8 cubic meters, a eigt of 8 meters, ad a legt of 4 meters. b 0. I te diagram, m = 5 ad bisects. xplai ow to fid m. G 58 Geometry opyrigt ig Ideas Learig, LL
4 Name ate.4 ricmet ad xtesio lgebraic Reasoig I xercises ad, solve for te idicated variable. Justify eac step. S = a + d. Solve for a: ( 3. Solve for r: V = π ( 3r ) Write a justificatio for eac step of te matematical iductio proof, wic proves tat 0 is divisible by 9. k a. 0 = 9r a. k b. 0 = 9r + b. c. 0( 0 k ) 0( 9r k d. 0 0( 9r = + c. + = + d. k + e. 0 = 90r + 0 e. k + f. 0 = 90r + 9 f. k g. 0 9( 0r + = + g. 4. Suppose you receive a raise at work. Your curret wage (i dollars per our) is represeted by c, te percet icrease (as a decimal) i your wage is represeted by r, ad your ew wage (i dollars per our) is represeted by. a. Use te give iformatio to write a pay raise formula tat you ca use to calculate your ew wage. b. Solve te formula from part (a) for r ad write a reaso for eac step. c. Use te result for part (b) to fid your percet icrease if your curret wage is $0.50 ad your ew wage will be $0.7. d. Suppose your co-worker receives a 4% pay raise ad er ew wage is $0.4. id your co-worker s old wage. xplai te steps you used to fid your aswer. opyrigt ig Ideas Learig, LL Geometry 59
5 Name ate.4 Puzzle Time How a You Sare ive pples Wit Seve rieds? Write te letter of eac aswer i te box cotaiig te exercise umber. Idetify te algebraic properties of equality tat are represeted.. If a = b, te a c = b c, c 0.. If a = b, te a c = b c. If a = b, te a ca be substituted for b (or b for a) i ay equatio or expressio. 4. If, te a b a = b, c 0. c = c 5. If a = b, te a + c = b + c. 6. sum: ab ( + c) = ab+ ac, differece: ab ( c) = ab ac 7. If a = b ad b = c, te a = c. If = ad =, te =. If m = m ad m = m, te m = m. 8. If a = b, te b = a. If =, te =. If m = m, te m = m. 9. a = a, =, m = m swers. Subtractio R. I. Iverse P. Multiplicatio Q. I. dditio M. Substitutio. overse. G. ivisio. istributive. Trasformatio V. H. Trasitive. Symmetric P. M. Reverse. Reflexive L. O. lgebraic S. U. K. Matc te property of equality to te statemet it illustrates. () Reflexive, () Subtractio, () istributive, () Multiplicatio, () Trasitive, () Symmetric, (G) ivisio, (H) dditio, (I) Substitutio 0. If x = y, te 6x = 6 y.. If =, te =.. m = m If = ad = 6, te = If a = b, te b = a Geometry opyrigt ig Ideas Learig, LL
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