1098 MATH - ALGEBRA I (PACE)

WRITE THE ALGEBRAIC SYMBOLS... Three more than the sum of x and y

(x+y)+3 or 3+(x+y)

WRITE THE ALGEBRAIC SYMBOLS... c subtracted from the sum of x and y

(x+y)-c

WRITE THE ALGEBRAIC EXPRESSION... One-third the sum of x, y, and z

1/3(x+y+z)

12x - 16 = 8 + 6x

12x-6x-16=8+6x-6x 6x-16=8 6x-16+16=8+16 6x=24 divide by 6 x=4

18 - (x+3) - 2x = 4 + (x-5)

18-x-3-2x=4+x-5 -x-2x+18-3=x+4-5 -3x+15=x-1 -3x-x+15-15=x-x-1-15 -4x=-16 divide by -4 x=4

1/2x = 12

2(1/2x)=2(12) x=24

WRITE THE ALGEBRAIC EXPRESSION... The sum of two numbers subtracted from twice the sum of those numbers

2(x+y)-(x+y)

20 + x = 4 + 2x

20+x-2x=4+2x-2x 20-x=4 20-20-x=4-20 -x=-16 divide by -1 x=16

28 + x = 7 - 2x

28+x+2x=7-2x+2x 28+3x=7 28-28+3x=7-28 3x=-21 (divide by 3) x=-7

2x = 25 + 3x

2x-3x=25=3x-3x -x=25 -1(-x)=-1(25) x=-25

1/3x = 15

3(1/3x)=3(15) x=45

3(x+2) - 2(2x-4) = 28

3x+3(2)-2(2x)-2(-14)=28 3x+6-4x+8=28 3x-4x+6+8=28 -x+14=28 -x+14-14=28-14 -x=14 divide by -1 x=-14

5(x-3) + 2(3-x) = 12

5x + 5(-3) + 2(3) + 2 (-x) = 12 5x-15+6-2x=12 5x-2x-15+6=12 3x-9=12 3x-9+9=12+9 3x=21 divide by 3 x=7

Number in order these steps for solving an equation... __________ Verify __________ Combine terms __________ Transpose terms __________ Divide by the coefficient of x __________ Remove parentheses __________ Simplify

6 4 3 5 1 2

9(2x+5) + 6 = 6 + 3x

9(2x)+9(5)+6=6+3x (minus 6) 18x+45=3x 18x-3x+45-45=3x-3x-45 15x=-45 divide by 15 x= -3

JOSHUA 24:15

And if it seem evil unto you to serve the Lord, Choose you this day whom ye will serve; whether the gods which your fathers served that were on the other side of the flood, or the gods of the Amorites, in whose land ye dwell: but as for me and my house, we will serve the Lord.

The degree measure of the angels of a certain triangle are consecutive even integers. What are the degree measures of the three angles?

Let x = degree measure of 1st angle x+2 = degree measure of 2nd angle x+4 = degree measure of 3td angle x+(x+2)+(x+4) = 180 x+x+2+x+4=180 3x+6=180 3x+6-6=180-6 3x=174 divide by 3 x=58 first angle 58+2=60 second angle 58+4=62 third angle

If three-fourths of a man's age is 36 years, how old is he?

Let x= man's age 3/4x=36 4(3/4x)=4(36) 3x=144 divide by 3 x=48

The sum of two numbers is 133. Four times the smaller of the two numbers equals three times the greater number. Find the numbers.

Let x= smaller number 133-x=greater number 4x=3(133-x) 4x=3(133)+3(-x) 4x=399-3x 4x+3x=399-3x+3x 7x=399 divide by 7 x=57 smaller number 133-x 133-57= 76 greater number

Three times a certain number is 46 more than the number itself. Find the number.

Let x= the number 3x=x+46 3x-x=x-x+46 2x=46 divide by 2 x=23

If 18 is added to the sum of three consecutive integers, the result is 168. What are the integers?

Let x=1st integer x+1=2nd integer x+2=3rd integer x+(x+1)+(x+2)+18=168 x+x+1+x+2+18=168 x+x+x+1+2+18=168 3x+21=168 3x+21-21=168-21 3x=147 divide by 3 x=49 1st integer x+1 49+1 = 50 2nd integer x+2 49+2= 51 3rd integer

The sum of two consecutive even integers is 122. What are the integers?

Let x=1st integer x+2=2nd integer x+(x+2)=122 x+x+2=122 2x+2=122 2x+2-2=122-2 2x=120 divide by 2 x=60 1st integer x+2 60+2=62 2nd integer

In 8 years, a girl will be 3 years older than twice her present age. How old is she now?

Let x=girl's present age x+8=2x+3 x-2x+8-8=2x-2x+3-8 -x=-5 x=5

Ace's grandfather is 3 years older than Ace's grandmother. Their combined age is 121 years. How old is each?

Let x=grandmother's age x+3=grandfather's age x+(x+3)=121 x+x+3=121 2x+3=121 2x+3-3=121-3 2x=118 divide by 2 x=59 grandmother x+3= 59+3=62 grandfather

In a group of 180 persons composed of men, women, and children, there are twice as many men as women, and three times as many women as children. How many are there of each?

Let x=number of children 3x=number of women 2(3x)=number of men x+3x+2(3x)=180 x+3x+6x=180 10x=180 divide by 10 x=18 children 3x 3(18)=54 women 2(3x) 2*3*18= 108 men

A boy's age is three times the age of his sister. Their ages together total 16 years. What is the age of each?

Let x=sister's age 3x=boy's age x+3x=16 4x=16 divide by 4 x=4 sister's age 3x 3(4)= 12 boy's age

The difference of two numbers is 18, and their sum is 90. Find the two numbers.

Let x=smaller number 18+x=greater number x+(18+x)=90 x+18+x=90 x+x+18=90 2x+18=90 2x+18-18=90-18 2x=72 divide by 2 x=36 smaller number 18+x= 18+36 = 54 greater number

The sum of two numbers is 208. One-third of the greater number equals the smaller number. What are the numbers?

Let x=smaller number 208-x=greater number 1/3(208-x) = x 3(1/3)(208-x)=3x 1(208-x)=3x 208-x=3x 208-208-x-3x=3x-3x-208 -4x=-208 divide by -4 x=52 smaller number 208-x 208-52 = 156 greater number

If a certain number is added to 36, the result is the same as if the number were multiplied by 4. What is the number?

Let x=the number 36+x=4x 36-36+x-4x=4x-4x-36 -3x=-36 divide by -3 x=12

If two-thirds of a woman's age is 42, how old is she?

Let x=woman's age 2/3x=42 3(2/3x)=3(42) 2x=126 divide by 2 x=63

In solving equations, it is important that __________ signs be kept vertically aligned.

equal

x - 3/5 = 2/5 +5

multiply everything by 5 5x-5(3/5)=5(2/5)+5(5) 5x-3=2+25 5x-3=27 5x-3+3=27+3 5x=30 divide by 5 x=6

The value which satisfies the algebraic equation is the __________ .

root or solution

Moving all the terms containing the unknown to the left of the equal sign and all other terms to the right of the equal sign is called __________ terms.

transposing

WRITE THE ALGEBRAIC EXPRESSION... If the difference of two numbers is a and the smaller number is x, what is the greater number?

x+a or z+x

x - 5 = 30

x-5+5=30+5 x=35

WRITE THE ALGEBRAIC SYMBOLS... If one addend of x is c, what is the other addend?

x-c

WRITE THE ALGEBRAIC EXPRESSION... x decreased by y

x-y