Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{3}{5})& = & 5x+\frac{5}{6} \\\Leftrightarrow & -9x-\frac{9}{5}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-270}{ \color{blue}{30} }x- \frac{54}{ \color{blue}{30} })& = & (\frac{150}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -270x \color{red}{-54} & = & \color{red}{150x} +25 \\\Leftrightarrow & -270x \color{red}{-54} \color{blue}{+54} \color{blue}{-150x} & = & \color{red}{150x} +25 \color{blue}{-150x} \color{blue}{+54} \\\Leftrightarrow & -270x-150x& = & 25+54 \\\Leftrightarrow & \color{red}{-420} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-420} & & \\\Leftrightarrow & x = \frac{-79}{420} & & \\ & V = \left\{ \frac{-79}{420} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{2}{11})& = & -2x+\frac{6}{11} \\\Leftrightarrow & 15x+\frac{6}{11}& = & -2x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{165}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} })& = & (\frac{-22}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 165x \color{red}{+6} & = & \color{red}{-22x} +6 \\\Leftrightarrow & 165x \color{red}{+6} \color{blue}{-6} \color{blue}{+22x} & = & \color{red}{-22x} +6 \color{blue}{+22x} \color{blue}{-6} \\\Leftrightarrow & 165x+22x& = & 6-6 \\\Leftrightarrow & \color{red}{187} x& = & 0 \\\Leftrightarrow & x = \frac{0}{187} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{5}{11})& = & 7x+\frac{7}{8} \\\Leftrightarrow & -6x-\frac{15}{11}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-528}{ \color{blue}{88} }x- \frac{120}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -528x \color{red}{-120} & = & \color{red}{616x} +77 \\\Leftrightarrow & -528x \color{red}{-120} \color{blue}{+120} \color{blue}{-616x} & = & \color{red}{616x} +77 \color{blue}{-616x} \color{blue}{+120} \\\Leftrightarrow & -528x-616x& = & 77+120 \\\Leftrightarrow & \color{red}{-1144} x& = & 197 \\\Leftrightarrow & x = \frac{197}{-1144} & & \\\Leftrightarrow & x = \frac{-197}{1144} & & \\ & V = \left\{ \frac{-197}{1144} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{5}{11})& = & 7x+\frac{2}{11} \\\Leftrightarrow & -6x-\frac{15}{11}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-66}{ \color{blue}{11} }x- \frac{15}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -66x \color{red}{-15} & = & \color{red}{77x} +2 \\\Leftrightarrow & -66x \color{red}{-15} \color{blue}{+15} \color{blue}{-77x} & = & \color{red}{77x} +2 \color{blue}{-77x} \color{blue}{+15} \\\Leftrightarrow & -66x-77x& = & 2+15 \\\Leftrightarrow & \color{red}{-143} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-143} & & \\\Leftrightarrow & x = \frac{-17}{143} & & \\ & V = \left\{ \frac{-17}{143} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{3}{7})& = & 3x+\frac{3}{10} \\\Leftrightarrow & -20x+\frac{15}{7}& = & 3x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1400}{ \color{blue}{70} }x+ \frac{150}{ \color{blue}{70} })& = & (\frac{210}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1400x \color{red}{+150} & = & \color{red}{210x} +21 \\\Leftrightarrow & -1400x \color{red}{+150} \color{blue}{-150} \color{blue}{-210x} & = & \color{red}{210x} +21 \color{blue}{-210x} \color{blue}{-150} \\\Leftrightarrow & -1400x-210x& = & 21-150 \\\Leftrightarrow & \color{red}{-1610} x& = & -129 \\\Leftrightarrow & x = \frac{-129}{-1610} & & \\\Leftrightarrow & x = \frac{129}{1610} & & \\ & V = \left\{ \frac{129}{1610} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{2}{3})& = & -2x+\frac{6}{5} \\\Leftrightarrow & -28x+\frac{14}{3}& = & -2x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-420}{ \color{blue}{15} }x+ \frac{70}{ \color{blue}{15} })& = & (\frac{-30}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -420x \color{red}{+70} & = & \color{red}{-30x} +18 \\\Leftrightarrow & -420x \color{red}{+70} \color{blue}{-70} \color{blue}{+30x} & = & \color{red}{-30x} +18 \color{blue}{+30x} \color{blue}{-70} \\\Leftrightarrow & -420x+30x& = & 18-70 \\\Leftrightarrow & \color{red}{-390} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{-390} & & \\\Leftrightarrow & x = \frac{2}{15} & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{5}{3})& = & 9x+\frac{5}{11} \\\Leftrightarrow & -8x+\frac{20}{3}& = & 9x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{+220} & = & \color{red}{297x} +15 \\\Leftrightarrow & -264x \color{red}{+220} \color{blue}{-220} \color{blue}{-297x} & = & \color{red}{297x} +15 \color{blue}{-297x} \color{blue}{-220} \\\Leftrightarrow & -264x-297x& = & 15-220 \\\Leftrightarrow & \color{red}{-561} x& = & -205 \\\Leftrightarrow & x = \frac{-205}{-561} & & \\\Leftrightarrow & x = \frac{205}{561} & & \\ & V = \left\{ \frac{205}{561} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{2}{11})& = & 3x+\frac{8}{11} \\\Leftrightarrow & 10x-\frac{4}{11}& = & 3x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{110}{ \color{blue}{11} }x- \frac{4}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 110x \color{red}{-4} & = & \color{red}{33x} +8 \\\Leftrightarrow & 110x \color{red}{-4} \color{blue}{+4} \color{blue}{-33x} & = & \color{red}{33x} +8 \color{blue}{-33x} \color{blue}{+4} \\\Leftrightarrow & 110x-33x& = & 8+4 \\\Leftrightarrow & \color{red}{77} x& = & 12 \\\Leftrightarrow & x = \frac{12}{77} & & \\ & V = \left\{ \frac{12}{77} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{5}{8})& = & -6x+\frac{9}{10} \\\Leftrightarrow & -35x-\frac{35}{8}& = & -6x+\frac{9}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1400}{ \color{blue}{40} }x- \frac{175}{ \color{blue}{40} })& = & (\frac{-240}{ \color{blue}{40} }x+ \frac{36}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1400x \color{red}{-175} & = & \color{red}{-240x} +36 \\\Leftrightarrow & -1400x \color{red}{-175} \color{blue}{+175} \color{blue}{+240x} & = & \color{red}{-240x} +36 \color{blue}{+240x} \color{blue}{+175} \\\Leftrightarrow & -1400x+240x& = & 36+175 \\\Leftrightarrow & \color{red}{-1160} x& = & 211 \\\Leftrightarrow & x = \frac{211}{-1160} & & \\\Leftrightarrow & x = \frac{-211}{1160} & & \\ & V = \left\{ \frac{-211}{1160} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{2}{11})& = & -3x+\frac{6}{11} \\\Leftrightarrow & 16x-\frac{8}{11}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{176}{ \color{blue}{11} }x- \frac{8}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 176x \color{red}{-8} & = & \color{red}{-33x} +6 \\\Leftrightarrow & 176x \color{red}{-8} \color{blue}{+8} \color{blue}{+33x} & = & \color{red}{-33x} +6 \color{blue}{+33x} \color{blue}{+8} \\\Leftrightarrow & 176x+33x& = & 6+8 \\\Leftrightarrow & \color{red}{209} x& = & 14 \\\Leftrightarrow & x = \frac{14}{209} & & \\ & V = \left\{ \frac{14}{209} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{5}{8})& = & 5x+\frac{4}{5} \\\Leftrightarrow & 12x+\frac{15}{8}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{480}{ \color{blue}{40} }x+ \frac{75}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{32}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 480x \color{red}{+75} & = & \color{red}{200x} +32 \\\Leftrightarrow & 480x \color{red}{+75} \color{blue}{-75} \color{blue}{-200x} & = & \color{red}{200x} +32 \color{blue}{-200x} \color{blue}{-75} \\\Leftrightarrow & 480x-200x& = & 32-75 \\\Leftrightarrow & \color{red}{280} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{280} & & \\ & V = \left\{ \frac{-43}{280} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{3}{4})& = & -3x+\frac{7}{2} \\\Leftrightarrow & 10x-\frac{15}{4}& = & -3x+\frac{7}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{40}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{-12}{ \color{blue}{4} }x+ \frac{14}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 40x \color{red}{-15} & = & \color{red}{-12x} +14 \\\Leftrightarrow & 40x \color{red}{-15} \color{blue}{+15} \color{blue}{+12x} & = & \color{red}{-12x} +14 \color{blue}{+12x} \color{blue}{+15} \\\Leftrightarrow & 40x+12x& = & 14+15 \\\Leftrightarrow & \color{red}{52} x& = & 29 \\\Leftrightarrow & x = \frac{29}{52} & & \\ & V = \left\{ \frac{29}{52} \right\} & \\\end{align}\)