Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

1. \(-5(-4x-1)=-7x+\frac{3}{10}\)
2. \(7(-5x+\frac{5}{4})=-3x+\frac{3}{2}\)
3. \(5(4x+\frac{2}{7})=9x+\frac{6}{11}\)
4. \(-2(-5x-\frac{3}{7})=-7x+\frac{10}{3}\)
5. \(5(5x+\frac{2}{9})=6x+\frac{7}{12}\)
6. \(-4(5x-\frac{4}{7})=-3x+\frac{8}{7}\)
7. \(7(3x-\frac{4}{9})=8x+\frac{10}{3}\)
8. \(4(-4x+\frac{4}{5})=7x+\frac{8}{11}\)
9. \(-3(-3x+\frac{3}{5})=4x+\frac{6}{7}\)
10. \(3(3x-\frac{2}{11})=4x+\frac{4}{3}\)
11. \(-6(2x-\frac{4}{11})=5x+\frac{4}{9}\)
12. \(-5(-3x+\frac{4}{9})=4x+\frac{10}{11}\)

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-1)& = & -7x+\frac{3}{10} \\\Leftrightarrow & 20x+5& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 1 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{200}{ \color{blue}{10} }x+ \frac{50}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 200x \color{red}{+50} & = & \color{red}{-70x} +3 \\\Leftrightarrow & 200x \color{red}{+50} \color{blue}{-50} \color{blue}{+70x} & = & \color{red}{-70x} +3 \color{blue}{+70x} \color{blue}{-50} \\\Leftrightarrow & 200x+70x& = & 3-50 \\\Leftrightarrow & \color{red}{270} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{270} & & \\ & V = \left\{ \frac{-47}{270} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{5}{4})& = & -3x+\frac{3}{2} \\\Leftrightarrow & -35x+\frac{35}{4}& = & -3x+\frac{3}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-140}{ \color{blue}{4} }x+ \frac{35}{ \color{blue}{4} })& = & (\frac{-12}{ \color{blue}{4} }x+ \frac{6}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -140x \color{red}{+35} & = & \color{red}{-12x} +6 \\\Leftrightarrow & -140x \color{red}{+35} \color{blue}{-35} \color{blue}{+12x} & = & \color{red}{-12x} +6 \color{blue}{+12x} \color{blue}{-35} \\\Leftrightarrow & -140x+12x& = & 6-35 \\\Leftrightarrow & \color{red}{-128} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-128} & & \\\Leftrightarrow & x = \frac{29}{128} & & \\ & V = \left\{ \frac{29}{128} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{2}{7})& = & 9x+\frac{6}{11} \\\Leftrightarrow & 20x+\frac{10}{7}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{+110} & = & \color{red}{693x} +42 \\\Leftrightarrow & 1540x \color{red}{+110} \color{blue}{-110} \color{blue}{-693x} & = & \color{red}{693x} +42 \color{blue}{-693x} \color{blue}{-110} \\\Leftrightarrow & 1540x-693x& = & 42-110 \\\Leftrightarrow & \color{red}{847} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{847} & & \\ & V = \left\{ \frac{-68}{847} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{3}{7})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 10x+\frac{6}{7}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{+18} & = & \color{red}{-147x} +70 \\\Leftrightarrow & 210x \color{red}{+18} \color{blue}{-18} \color{blue}{+147x} & = & \color{red}{-147x} +70 \color{blue}{+147x} \color{blue}{-18} \\\Leftrightarrow & 210x+147x& = & 70-18 \\\Leftrightarrow & \color{red}{357} x& = & 52 \\\Leftrightarrow & x = \frac{52}{357} & & \\ & V = \left\{ \frac{52}{357} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{2}{9})& = & 6x+\frac{7}{12} \\\Leftrightarrow & 25x+\frac{10}{9}& = & 6x+\frac{7}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{900}{ \color{blue}{36} }x+ \frac{40}{ \color{blue}{36} })& = & (\frac{216}{ \color{blue}{36} }x+ \frac{21}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 900x \color{red}{+40} & = & \color{red}{216x} +21 \\\Leftrightarrow & 900x \color{red}{+40} \color{blue}{-40} \color{blue}{-216x} & = & \color{red}{216x} +21 \color{blue}{-216x} \color{blue}{-40} \\\Leftrightarrow & 900x-216x& = & 21-40 \\\Leftrightarrow & \color{red}{684} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{684} & & \\\Leftrightarrow & x = \frac{-1}{36} & & \\ & V = \left\{ \frac{-1}{36} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{4}{7})& = & -3x+\frac{8}{7} \\\Leftrightarrow & -20x+\frac{16}{7}& = & -3x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-140}{ \color{blue}{7} }x+ \frac{16}{ \color{blue}{7} })& = & (\frac{-21}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -140x \color{red}{+16} & = & \color{red}{-21x} +8 \\\Leftrightarrow & -140x \color{red}{+16} \color{blue}{-16} \color{blue}{+21x} & = & \color{red}{-21x} +8 \color{blue}{+21x} \color{blue}{-16} \\\Leftrightarrow & -140x+21x& = & 8-16 \\\Leftrightarrow & \color{red}{-119} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-119} & & \\\Leftrightarrow & x = \frac{8}{119} & & \\ & V = \left\{ \frac{8}{119} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{4}{9})& = & 8x+\frac{10}{3} \\\Leftrightarrow & 21x-\frac{28}{9}& = & 8x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{189}{ \color{blue}{9} }x- \frac{28}{ \color{blue}{9} })& = & (\frac{72}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 189x \color{red}{-28} & = & \color{red}{72x} +30 \\\Leftrightarrow & 189x \color{red}{-28} \color{blue}{+28} \color{blue}{-72x} & = & \color{red}{72x} +30 \color{blue}{-72x} \color{blue}{+28} \\\Leftrightarrow & 189x-72x& = & 30+28 \\\Leftrightarrow & \color{red}{117} x& = & 58 \\\Leftrightarrow & x = \frac{58}{117} & & \\ & V = \left\{ \frac{58}{117} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{4}{5})& = & 7x+\frac{8}{11} \\\Leftrightarrow & -16x+\frac{16}{5}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-880}{ \color{blue}{55} }x+ \frac{176}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -880x \color{red}{+176} & = & \color{red}{385x} +40 \\\Leftrightarrow & -880x \color{red}{+176} \color{blue}{-176} \color{blue}{-385x} & = & \color{red}{385x} +40 \color{blue}{-385x} \color{blue}{-176} \\\Leftrightarrow & -880x-385x& = & 40-176 \\\Leftrightarrow & \color{red}{-1265} x& = & -136 \\\Leftrightarrow & x = \frac{-136}{-1265} & & \\\Leftrightarrow & x = \frac{136}{1265} & & \\ & V = \left\{ \frac{136}{1265} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{3}{5})& = & 4x+\frac{6}{7} \\\Leftrightarrow & 9x-\frac{9}{5}& = & 4x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{315}{ \color{blue}{35} }x- \frac{63}{ \color{blue}{35} })& = & (\frac{140}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 315x \color{red}{-63} & = & \color{red}{140x} +30 \\\Leftrightarrow & 315x \color{red}{-63} \color{blue}{+63} \color{blue}{-140x} & = & \color{red}{140x} +30 \color{blue}{-140x} \color{blue}{+63} \\\Leftrightarrow & 315x-140x& = & 30+63 \\\Leftrightarrow & \color{red}{175} x& = & 93 \\\Leftrightarrow & x = \frac{93}{175} & & \\ & V = \left\{ \frac{93}{175} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{2}{11})& = & 4x+\frac{4}{3} \\\Leftrightarrow & 9x-\frac{6}{11}& = & 4x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{297}{ \color{blue}{33} }x- \frac{18}{ \color{blue}{33} })& = & (\frac{132}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 297x \color{red}{-18} & = & \color{red}{132x} +44 \\\Leftrightarrow & 297x \color{red}{-18} \color{blue}{+18} \color{blue}{-132x} & = & \color{red}{132x} +44 \color{blue}{-132x} \color{blue}{+18} \\\Leftrightarrow & 297x-132x& = & 44+18 \\\Leftrightarrow & \color{red}{165} x& = & 62 \\\Leftrightarrow & x = \frac{62}{165} & & \\ & V = \left\{ \frac{62}{165} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{4}{11})& = & 5x+\frac{4}{9} \\\Leftrightarrow & -12x+\frac{24}{11}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1188}{ \color{blue}{99} }x+ \frac{216}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1188x \color{red}{+216} & = & \color{red}{495x} +44 \\\Leftrightarrow & -1188x \color{red}{+216} \color{blue}{-216} \color{blue}{-495x} & = & \color{red}{495x} +44 \color{blue}{-495x} \color{blue}{-216} \\\Leftrightarrow & -1188x-495x& = & 44-216 \\\Leftrightarrow & \color{red}{-1683} x& = & -172 \\\Leftrightarrow & x = \frac{-172}{-1683} & & \\\Leftrightarrow & x = \frac{172}{1683} & & \\ & V = \left\{ \frac{172}{1683} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{9})& = & 4x+\frac{10}{11} \\\Leftrightarrow & 15x-\frac{20}{9}& = & 4x+\frac{10}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1485}{ \color{blue}{99} }x- \frac{220}{ \color{blue}{99} })& = & (\frac{396}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1485x \color{red}{-220} & = & \color{red}{396x} +90 \\\Leftrightarrow & 1485x \color{red}{-220} \color{blue}{+220} \color{blue}{-396x} & = & \color{red}{396x} +90 \color{blue}{-396x} \color{blue}{+220} \\\Leftrightarrow & 1485x-396x& = & 90+220 \\\Leftrightarrow & \color{red}{1089} x& = & 310 \\\Leftrightarrow & x = \frac{310}{1089} & & \\ & V = \left\{ \frac{310}{1089} \right\} & \\\end{align}\)