30,000 is he answer hope it work
The answer is: "100" .
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Explanation:
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Looking at the ENTIRE EQUATION (all numeric values on BOTH sides of the equation), we can see that the decimal that with the most decimal places goes to the right, to the hundredths place (i.e. two places); so by multiplying the ENTIRE EQUATION (BOTH SIDES—i.e. EACH term on EACH SIDE) by "100", we get rid of ALL the decimals, as follows:
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100* {<span>5.6j – 0.12 = 41.1 j ) ;
</span>↔ (100* 5.6j) – (100 * 0.12) = (100 * 41.1 j );
↔ 560 j – 12 = 4110 j ;
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Answers:
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1) [B]: {-5, 5}
2) [A]: {-24, 8}
3) [C]: {-1, 4}
4) [A]: {-21, 15}
5) [C]: {-5/3, 3}
6) [A]: {⅔, 2}
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Explanation:
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2) "Solve: | m + 8| = 16 "; Assuming we are to solve for "m"; we would use:
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"Case 1" and "Case 2" scenarios;
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since we need to find the value for "m" when:
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Case 1: (m + 8) = 16; AND:
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Case 2: - (m + 8) = 16 .
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→ Let's solve, starting with Case 1:
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m + 8 = 16; → Subtract "8" from EACH SIDE of the equation;
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→ m + 8 − 8 = 16 − 8 ; → To get: → m = 8
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→ Let us solve for "Case 2" :
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- (m + 8) = 16 ;
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Note the distributive property of multiplication:
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→ a*(b + c) = ab + ac ;
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→ As such: - (m + 8) = 16 ;
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Consider this equation as:
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- 1(m + 8) = 16 ;
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→ Note the "-1" is implied, since anything multiplied by "1" is that same thing. The "negative" in the "negative 1" comes from the "negative sign" already present.
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→ - 1(m + 8) = 16 ; → (-1*m) + (-1*8) = 16 ;
→ -1m + (-8) = 16 ; → Rewrite as: -1m − 8 = 16 ;
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→ Add "8" to EACH SIDE of the equation ; → -1m − 8 + 8 = 16 + 8 ;
→ to get: -1m = 24 ;
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→ Divide EACH SIDE of the equation by "-1"; to isolate "m" on one side of the equation; & to solve for "m" ; → -1m / -1 = 24 / -1 ; → m = -24
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So we have: m = 8; and m = -24 ; which is: "Answer choice: [A]: {-24, 8}" .
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3) Given: |2n - 3| = 5 ; Solve for "n" ;
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Case 1: 2n − 3 = 5 ;
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→ Add "3" to EACH side of the equation; 2n − 3 + 3 = 5 + 3 ; → 2n = 8 ;
→ Now, divide EACH SIDE of the equation by "2"; to isolate "n" on one side of the equation; and to solve for "n"; → 2n / 2 = 8 / 2 ; → n = 4 .
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Case 2: - (2n − 3) = 5 ;
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Simplify: - (2n − 3); → - 1(2n − 3) = (-1*2n) − (-1*3) = -2n − (-3) = -2n + 3 ;
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→ Rewrite the equation, "- (2n − 3) = 5 " ; as:
→ -2n + 3 = 5; → Now, subtract "3" from EACH side of the equation:
→ -2n + 3 − 3 = 5 − 3 ; → -2n = 2 ;
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→ Divide EACH SIDE of the equation by "-2"; to isolate "n" on one side of the equation; and to solve for "n" ; → -2n / -2 = 2 / -2 ; → n = -1 .
→ So, n = 4, AND -1; which is: Answer choice: [C]: {-1, 4} .
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4) Given: |x/3 + 1| = 6 ; Solve for "x";
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Case 1: (x/3) + 1 = 6; Subtract "1" from EACH side of the equation;
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→ (x/3) + 1 − 1 = 6 − 1 ; → (x/3) = 5 ; → x = 5*3 = 15
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Case 2: - [ (x/3) + 1] = 6; → -1 [(x/3) + 1] = 6 ; → [-1*(x/3) ] + (-1*1) = 6 ;
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→ - (x/3) + (-1) = 6 ; → - (x/3) − 1 = 6 ;
→ Add "1" to EACH side of the equation:
→ - (x/3) − 1 + 1 = 6 + 1 ; → - (x/3) − 1 + 1 = 6 + 1 ;
→ - (x/3) = 7 ↔ -x / 3 = 7; -1x = 7*3 ; → -1x = 21;
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→ Divide EACH SIDE of the equation by "-1"; to isolate "x" on one side of the equation; & to solve for "x" ;
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→ -1x / -1 = 21 / -1 ; → x = -21;
So, x = 15, AND -21; which is: Answer choice: [A]: {-21, 15} .
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5) Given: |2 − 3x| = 7 ; Solve for "x";
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Case 1: (2 − 3x) = 7
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Given: 2 − 3x = 7 ; → Subtract "2" from EACH side of the equation;
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→ 2 − 3x − 2 = 7 − 2 ; → to get: -3x = 5 ;
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→ Now, divide EACH side of the equation by "-3"; to isolate "x" on one side of the equation; and to solve for "x" ; → -3x / =3 = 5/ -3 = - (5/3).
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→Case 2: -(2 − 3x) = 7 ; Simplify,
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Note: The distributive property of multiplication:
→ a*(b + c) = ab + ac ; AND: → a*(b − c) = ab − ac ;
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→ - (2 − 3x) = 7 ; → -1(2 − 3x) = 7 ; → (-1*2) − (-1*3x) = 7 ;
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→ - 2 − (-3x) = 7 ; → - 2 + 3x = 7 ; → Add "2" to EACH side of the equation ;
→ - 2 + 3x + 2 = 7 + 2 ; → 3x = 9 ;
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→ Now, divide EACH side of the equation by "3"; to isolate "x" on one side of the equation; and to solve for "x" ; → 3x / 3 = 9 / 3 ; x = 3;
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So, x = - 5/3; AND 3; which is: Answer choice: [C]: {-5/3, 3} .
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6) Given: |2y − 2| = y ; Solve for "y";
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Case 1: 2y − 2 = y;
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→ Subtract "y" from EACH SIDE of the equation;
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→ 2y − 2 = y ; → 2y − 2 − y = y − y ; → y − 2 = 0 ;
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→ Add "2" to EACH SIDE of the equation; to isolate "y" on one side of the equation; & to solve for "y" ; → y − 2 + 2 = 0 + 2 ; → y = 2
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Case 2: - (2y − 2) = y
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→ Simplify: - (2y − 2); → -1(2y − 2) = (-1*2y) − (-1*2) = -2y - (-2) = -2y + 2 ;
→ Rewrite: - (2y − 2) = y ; as: → -2y + 2 = y ;
→ Add "2y" to EACH SIDE of the equation:
→ -2y + 2 + 2y = y + 2y ; → 2 = 3y ;
→ Now, divide EACH side of the equation by "3"; to isolate "y" on one side of the equation & to solve for "y" ;
→ 2 / 3 = 3y / 3 ; → ⅔ = y ↔ y = ⅔ ; so y = 2, AND ⅔; which is:
→ Answer choice: [A]: {⅔, 2}
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