Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-1)& = & 3x+\frac{10}{7} \\\Leftrightarrow & -28x+7& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 1 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-196}{ \color{blue}{7} }x+ \frac{49}{ \color{blue}{7} })& = & (\frac{21}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -196x \color{red}{+49} & = & \color{red}{21x} +10 \\\Leftrightarrow & -196x \color{red}{+49} \color{blue}{-49} \color{blue}{-21x} & = & \color{red}{21x} +10 \color{blue}{-21x} \color{blue}{-49} \\\Leftrightarrow & -196x-21x& = & 10-49 \\\Leftrightarrow & \color{red}{-217} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{-217} & & \\\Leftrightarrow & x = \frac{39}{217} & & \\ & V = \left\{ \frac{39}{217} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{3}{2})& = & 3x+\frac{4}{11} \\\Leftrightarrow & -14x-\frac{21}{2}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-308}{ \color{blue}{22} }x- \frac{231}{ \color{blue}{22} })& = & (\frac{66}{ \color{blue}{22} }x+ \frac{8}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -308x \color{red}{-231} & = & \color{red}{66x} +8 \\\Leftrightarrow & -308x \color{red}{-231} \color{blue}{+231} \color{blue}{-66x} & = & \color{red}{66x} +8 \color{blue}{-66x} \color{blue}{+231} \\\Leftrightarrow & -308x-66x& = & 8+231 \\\Leftrightarrow & \color{red}{-374} x& = & 239 \\\Leftrightarrow & x = \frac{239}{-374} & & \\\Leftrightarrow & x = \frac{-239}{374} & & \\ & V = \left\{ \frac{-239}{374} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{4}{11})& = & 5x+\frac{5}{7} \\\Leftrightarrow & -12x-\frac{12}{11}& = & 5x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-84} & = & \color{red}{385x} +55 \\\Leftrightarrow & -924x \color{red}{-84} \color{blue}{+84} \color{blue}{-385x} & = & \color{red}{385x} +55 \color{blue}{-385x} \color{blue}{+84} \\\Leftrightarrow & -924x-385x& = & 55+84 \\\Leftrightarrow & \color{red}{-1309} x& = & 139 \\\Leftrightarrow & x = \frac{139}{-1309} & & \\\Leftrightarrow & x = \frac{-139}{1309} & & \\ & V = \left\{ \frac{-139}{1309} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{5}{7})& = & -3x+\frac{3}{10} \\\Leftrightarrow & 4x-\frac{10}{7}& = & -3x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{280}{ \color{blue}{70} }x- \frac{100}{ \color{blue}{70} })& = & (\frac{-210}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 280x \color{red}{-100} & = & \color{red}{-210x} +21 \\\Leftrightarrow & 280x \color{red}{-100} \color{blue}{+100} \color{blue}{+210x} & = & \color{red}{-210x} +21 \color{blue}{+210x} \color{blue}{+100} \\\Leftrightarrow & 280x+210x& = & 21+100 \\\Leftrightarrow & \color{red}{490} x& = & 121 \\\Leftrightarrow & x = \frac{121}{490} & & \\ & V = \left\{ \frac{121}{490} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{5}{8})& = & 2x+\frac{2}{9} \\\Leftrightarrow & 15x+\frac{15}{8}& = & 2x+\frac{2}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1080}{ \color{blue}{72} }x+ \frac{135}{ \color{blue}{72} })& = & (\frac{144}{ \color{blue}{72} }x+ \frac{16}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1080x \color{red}{+135} & = & \color{red}{144x} +16 \\\Leftrightarrow & 1080x \color{red}{+135} \color{blue}{-135} \color{blue}{-144x} & = & \color{red}{144x} +16 \color{blue}{-144x} \color{blue}{-135} \\\Leftrightarrow & 1080x-144x& = & 16-135 \\\Leftrightarrow & \color{red}{936} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{936} & & \\ & V = \left\{ \frac{-119}{936} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{2}{3})& = & -7x+\frac{10}{11} \\\Leftrightarrow & -6x+\frac{4}{3}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-198}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -198x \color{red}{+44} & = & \color{red}{-231x} +30 \\\Leftrightarrow & -198x \color{red}{+44} \color{blue}{-44} \color{blue}{+231x} & = & \color{red}{-231x} +30 \color{blue}{+231x} \color{blue}{-44} \\\Leftrightarrow & -198x+231x& = & 30-44 \\\Leftrightarrow & \color{red}{33} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{33} & & \\ & V = \left\{ \frac{-14}{33} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{5}{11})& = & -9x+\frac{4}{11} \\\Leftrightarrow & -4x+\frac{10}{11}& = & -9x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-44}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -44x \color{red}{+10} & = & \color{red}{-99x} +4 \\\Leftrightarrow & -44x \color{red}{+10} \color{blue}{-10} \color{blue}{+99x} & = & \color{red}{-99x} +4 \color{blue}{+99x} \color{blue}{-10} \\\Leftrightarrow & -44x+99x& = & 4-10 \\\Leftrightarrow & \color{red}{55} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{55} & & \\ & V = \left\{ \frac{-6}{55} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{4}{11})& = & -8x+\frac{6}{11} \\\Leftrightarrow & -21x+\frac{28}{11}& = & -8x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-231}{ \color{blue}{11} }x+ \frac{28}{ \color{blue}{11} })& = & (\frac{-88}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -231x \color{red}{+28} & = & \color{red}{-88x} +6 \\\Leftrightarrow & -231x \color{red}{+28} \color{blue}{-28} \color{blue}{+88x} & = & \color{red}{-88x} +6 \color{blue}{+88x} \color{blue}{-28} \\\Leftrightarrow & -231x+88x& = & 6-28 \\\Leftrightarrow & \color{red}{-143} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-143} & & \\\Leftrightarrow & x = \frac{2}{13} & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{4}{3})& = & 2x+\frac{9}{10} \\\Leftrightarrow & 15x+\frac{20}{3}& = & 2x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{450}{ \color{blue}{30} }x+ \frac{200}{ \color{blue}{30} })& = & (\frac{60}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 450x \color{red}{+200} & = & \color{red}{60x} +27 \\\Leftrightarrow & 450x \color{red}{+200} \color{blue}{-200} \color{blue}{-60x} & = & \color{red}{60x} +27 \color{blue}{-60x} \color{blue}{-200} \\\Leftrightarrow & 450x-60x& = & 27-200 \\\Leftrightarrow & \color{red}{390} x& = & -173 \\\Leftrightarrow & x = \frac{-173}{390} & & \\ & V = \left\{ \frac{-173}{390} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{4}{9})& = & -5x+\frac{8}{5} \\\Leftrightarrow & -25x-\frac{20}{9}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1125}{ \color{blue}{45} }x- \frac{100}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{72}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1125x \color{red}{-100} & = & \color{red}{-225x} +72 \\\Leftrightarrow & -1125x \color{red}{-100} \color{blue}{+100} \color{blue}{+225x} & = & \color{red}{-225x} +72 \color{blue}{+225x} \color{blue}{+100} \\\Leftrightarrow & -1125x+225x& = & 72+100 \\\Leftrightarrow & \color{red}{-900} x& = & 172 \\\Leftrightarrow & x = \frac{172}{-900} & & \\\Leftrightarrow & x = \frac{-43}{225} & & \\ & V = \left\{ \frac{-43}{225} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{3}{11})& = & 3x+\frac{8}{5} \\\Leftrightarrow & 25x-\frac{15}{11}& = & 3x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1375}{ \color{blue}{55} }x- \frac{75}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1375x \color{red}{-75} & = & \color{red}{165x} +88 \\\Leftrightarrow & 1375x \color{red}{-75} \color{blue}{+75} \color{blue}{-165x} & = & \color{red}{165x} +88 \color{blue}{-165x} \color{blue}{+75} \\\Leftrightarrow & 1375x-165x& = & 88+75 \\\Leftrightarrow & \color{red}{1210} x& = & 163 \\\Leftrightarrow & x = \frac{163}{1210} & & \\ & V = \left\{ \frac{163}{1210} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{4}{3})& = & 7x+\frac{5}{8} \\\Leftrightarrow & 20x-\frac{20}{3}& = & 7x+\frac{5}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{480}{ \color{blue}{24} }x- \frac{160}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{15}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 480x \color{red}{-160} & = & \color{red}{168x} +15 \\\Leftrightarrow & 480x \color{red}{-160} \color{blue}{+160} \color{blue}{-168x} & = & \color{red}{168x} +15 \color{blue}{-168x} \color{blue}{+160} \\\Leftrightarrow & 480x-168x& = & 15+160 \\\Leftrightarrow & \color{red}{312} x& = & 175 \\\Leftrightarrow & x = \frac{175}{312} & & \\ & V = \left\{ \frac{175}{312} \right\} & \\\end{align}\)