Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{2}{3})& = & -8x+\frac{4}{5} \\\Leftrightarrow & -21x-\frac{14}{3}& = & -8x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-315}{ \color{blue}{15} }x- \frac{70}{ \color{blue}{15} })& = & (\frac{-120}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -315x \color{red}{-70} & = & \color{red}{-120x} +12 \\\Leftrightarrow & -315x \color{red}{-70} \color{blue}{+70} \color{blue}{+120x} & = & \color{red}{-120x} +12 \color{blue}{+120x} \color{blue}{+70} \\\Leftrightarrow & -315x+120x& = & 12+70 \\\Leftrightarrow & \color{red}{-195} x& = & 82 \\\Leftrightarrow & x = \frac{82}{-195} & & \\\Leftrightarrow & x = \frac{-82}{195} & & \\ & V = \left\{ \frac{-82}{195} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{4}{11})& = & 5x+\frac{9}{8} \\\Leftrightarrow & -12x+\frac{24}{11}& = & 5x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1056}{ \color{blue}{88} }x+ \frac{192}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1056x \color{red}{+192} & = & \color{red}{440x} +99 \\\Leftrightarrow & -1056x \color{red}{+192} \color{blue}{-192} \color{blue}{-440x} & = & \color{red}{440x} +99 \color{blue}{-440x} \color{blue}{-192} \\\Leftrightarrow & -1056x-440x& = & 99-192 \\\Leftrightarrow & \color{red}{-1496} x& = & -93 \\\Leftrightarrow & x = \frac{-93}{-1496} & & \\\Leftrightarrow & x = \frac{93}{1496} & & \\ & V = \left\{ \frac{93}{1496} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{5}{7})& = & 7x+\frac{3}{7} \\\Leftrightarrow & 8x+\frac{20}{7}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{56}{ \color{blue}{7} }x+ \frac{20}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 56x \color{red}{+20} & = & \color{red}{49x} +3 \\\Leftrightarrow & 56x \color{red}{+20} \color{blue}{-20} \color{blue}{-49x} & = & \color{red}{49x} +3 \color{blue}{-49x} \color{blue}{-20} \\\Leftrightarrow & 56x-49x& = & 3-20 \\\Leftrightarrow & \color{red}{7} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{7} & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{3}{10})& = & -5x+\frac{10}{7} \\\Leftrightarrow & -12x+\frac{9}{10}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 10 en 7 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-840}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} })& = & (\frac{-350}{ \color{blue}{70} }x+ \frac{100}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -840x \color{red}{+63} & = & \color{red}{-350x} +100 \\\Leftrightarrow & -840x \color{red}{+63} \color{blue}{-63} \color{blue}{+350x} & = & \color{red}{-350x} +100 \color{blue}{+350x} \color{blue}{-63} \\\Leftrightarrow & -840x+350x& = & 100-63 \\\Leftrightarrow & \color{red}{-490} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-490} & & \\\Leftrightarrow & x = \frac{-37}{490} & & \\ & V = \left\{ \frac{-37}{490} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{2}{7})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 12x+\frac{6}{7}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+66} & = & \color{red}{385x} +42 \\\Leftrightarrow & 924x \color{red}{+66} \color{blue}{-66} \color{blue}{-385x} & = & \color{red}{385x} +42 \color{blue}{-385x} \color{blue}{-66} \\\Leftrightarrow & 924x-385x& = & 42-66 \\\Leftrightarrow & \color{red}{539} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{539} & & \\ & V = \left\{ \frac{-24}{539} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{2}{5})& = & 5x+\frac{6}{11} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-132} & = & \color{red}{275x} +30 \\\Leftrightarrow & -660x \color{red}{-132} \color{blue}{+132} \color{blue}{-275x} & = & \color{red}{275x} +30 \color{blue}{-275x} \color{blue}{+132} \\\Leftrightarrow & -660x-275x& = & 30+132 \\\Leftrightarrow & \color{red}{-935} x& = & 162 \\\Leftrightarrow & x = \frac{162}{-935} & & \\\Leftrightarrow & x = \frac{-162}{935} & & \\ & V = \left\{ \frac{-162}{935} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{2}{5})& = & 3x+\frac{3}{11} \\\Leftrightarrow & 8x+\frac{4}{5}& = & 3x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{+44} & = & \color{red}{165x} +15 \\\Leftrightarrow & 440x \color{red}{+44} \color{blue}{-44} \color{blue}{-165x} & = & \color{red}{165x} +15 \color{blue}{-165x} \color{blue}{-44} \\\Leftrightarrow & 440x-165x& = & 15-44 \\\Leftrightarrow & \color{red}{275} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{275} & & \\ & V = \left\{ \frac{-29}{275} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{2}{3})& = & -5x+\frac{5}{6} \\\Leftrightarrow & 12x+\frac{8}{3}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{72}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{-30}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 72x \color{red}{+16} & = & \color{red}{-30x} +5 \\\Leftrightarrow & 72x \color{red}{+16} \color{blue}{-16} \color{blue}{+30x} & = & \color{red}{-30x} +5 \color{blue}{+30x} \color{blue}{-16} \\\Leftrightarrow & 72x+30x& = & 5-16 \\\Leftrightarrow & \color{red}{102} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{102} & & \\ & V = \left\{ \frac{-11}{102} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{5}{4})& = & -8x+\frac{7}{2} \\\Leftrightarrow & 15x-\frac{15}{4}& = & -8x+\frac{7}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{60}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{-32}{ \color{blue}{4} }x+ \frac{14}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 60x \color{red}{-15} & = & \color{red}{-32x} +14 \\\Leftrightarrow & 60x \color{red}{-15} \color{blue}{+15} \color{blue}{+32x} & = & \color{red}{-32x} +14 \color{blue}{+32x} \color{blue}{+15} \\\Leftrightarrow & 60x+32x& = & 14+15 \\\Leftrightarrow & \color{red}{92} x& = & 29 \\\Leftrightarrow & x = \frac{29}{92} & & \\ & V = \left\{ \frac{29}{92} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{4}{11})& = & 4x+\frac{9}{2} \\\Leftrightarrow & 15x-\frac{20}{11}& = & 4x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{330}{ \color{blue}{22} }x- \frac{40}{ \color{blue}{22} })& = & (\frac{88}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 330x \color{red}{-40} & = & \color{red}{88x} +99 \\\Leftrightarrow & 330x \color{red}{-40} \color{blue}{+40} \color{blue}{-88x} & = & \color{red}{88x} +99 \color{blue}{-88x} \color{blue}{+40} \\\Leftrightarrow & 330x-88x& = & 99+40 \\\Leftrightarrow & \color{red}{242} x& = & 139 \\\Leftrightarrow & x = \frac{139}{242} & & \\ & V = \left\{ \frac{139}{242} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{2}{11})& = & -8x+\frac{7}{3} \\\Leftrightarrow & -18x+\frac{12}{11}& = & -8x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-594}{ \color{blue}{33} }x+ \frac{36}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -594x \color{red}{+36} & = & \color{red}{-264x} +77 \\\Leftrightarrow & -594x \color{red}{+36} \color{blue}{-36} \color{blue}{+264x} & = & \color{red}{-264x} +77 \color{blue}{+264x} \color{blue}{-36} \\\Leftrightarrow & -594x+264x& = & 77-36 \\\Leftrightarrow & \color{red}{-330} x& = & 41 \\\Leftrightarrow & x = \frac{41}{-330} & & \\\Leftrightarrow & x = \frac{-41}{330} & & \\ & V = \left\{ \frac{-41}{330} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{2}{5})& = & 5x+\frac{8}{5} \\\Leftrightarrow & 24x+\frac{12}{5}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{120}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 120x \color{red}{+12} & = & \color{red}{25x} +8 \\\Leftrightarrow & 120x \color{red}{+12} \color{blue}{-12} \color{blue}{-25x} & = & \color{red}{25x} +8 \color{blue}{-25x} \color{blue}{-12} \\\Leftrightarrow & 120x-25x& = & 8-12 \\\Leftrightarrow & \color{red}{95} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{95} & & \\ & V = \left\{ \frac{-4}{95} \right\} & \\\end{align}\)