Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{2}{11})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 10x+\frac{10}{11}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{330}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 330x \color{red}{+30} & = & \color{red}{231x} +110 \\\Leftrightarrow & 330x \color{red}{+30} \color{blue}{-30} \color{blue}{-231x} & = & \color{red}{231x} +110 \color{blue}{-231x} \color{blue}{-30} \\\Leftrightarrow & 330x-231x& = & 110-30 \\\Leftrightarrow & \color{red}{99} x& = & 80 \\\Leftrightarrow & x = \frac{80}{99} & & \\ & V = \left\{ \frac{80}{99} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{2}{3})& = & -9x+\frac{5}{11} \\\Leftrightarrow & -8x-\frac{8}{3}& = & -9x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{-88} & = & \color{red}{-297x} +15 \\\Leftrightarrow & -264x \color{red}{-88} \color{blue}{+88} \color{blue}{+297x} & = & \color{red}{-297x} +15 \color{blue}{+297x} \color{blue}{+88} \\\Leftrightarrow & -264x+297x& = & 15+88 \\\Leftrightarrow & \color{red}{33} x& = & 103 \\\Leftrightarrow & x = \frac{103}{33} & & \\ & V = \left\{ \frac{103}{33} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{2}{5})& = & -9x+\frac{4}{7} \\\Leftrightarrow & -8x+\frac{4}{5}& = & -9x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{+28} & = & \color{red}{-315x} +20 \\\Leftrightarrow & -280x \color{red}{+28} \color{blue}{-28} \color{blue}{+315x} & = & \color{red}{-315x} +20 \color{blue}{+315x} \color{blue}{-28} \\\Leftrightarrow & -280x+315x& = & 20-28 \\\Leftrightarrow & \color{red}{35} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{35} & & \\ & V = \left\{ \frac{-8}{35} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{5}{11})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -10x+\frac{25}{11}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x+ \frac{75}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{+75} & = & \color{red}{-231x} +110 \\\Leftrightarrow & -330x \color{red}{+75} \color{blue}{-75} \color{blue}{+231x} & = & \color{red}{-231x} +110 \color{blue}{+231x} \color{blue}{-75} \\\Leftrightarrow & -330x+231x& = & 110-75 \\\Leftrightarrow & \color{red}{-99} x& = & 35 \\\Leftrightarrow & x = \frac{35}{-99} & & \\\Leftrightarrow & x = \frac{-35}{99} & & \\ & V = \left\{ \frac{-35}{99} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{4}{11})& = & -3x+\frac{9}{11} \\\Leftrightarrow & -35x-\frac{28}{11}& = & -3x+\frac{9}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-385}{ \color{blue}{11} }x- \frac{28}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{9}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -385x \color{red}{-28} & = & \color{red}{-33x} +9 \\\Leftrightarrow & -385x \color{red}{-28} \color{blue}{+28} \color{blue}{+33x} & = & \color{red}{-33x} +9 \color{blue}{+33x} \color{blue}{+28} \\\Leftrightarrow & -385x+33x& = & 9+28 \\\Leftrightarrow & \color{red}{-352} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-352} & & \\\Leftrightarrow & x = \frac{-37}{352} & & \\ & V = \left\{ \frac{-37}{352} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{7})& = & -3x+\frac{4}{7} \\\Leftrightarrow & 20x-\frac{20}{7}& = & -3x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{140}{ \color{blue}{7} }x- \frac{20}{ \color{blue}{7} })& = & (\frac{-21}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 140x \color{red}{-20} & = & \color{red}{-21x} +4 \\\Leftrightarrow & 140x \color{red}{-20} \color{blue}{+20} \color{blue}{+21x} & = & \color{red}{-21x} +4 \color{blue}{+21x} \color{blue}{+20} \\\Leftrightarrow & 140x+21x& = & 4+20 \\\Leftrightarrow & \color{red}{161} x& = & 24 \\\Leftrightarrow & x = \frac{24}{161} & & \\ & V = \left\{ \frac{24}{161} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{4}{3})& = & -9x+\frac{4}{7} \\\Leftrightarrow & -28x-\frac{28}{3}& = & -9x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-588}{ \color{blue}{21} }x- \frac{196}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -588x \color{red}{-196} & = & \color{red}{-189x} +12 \\\Leftrightarrow & -588x \color{red}{-196} \color{blue}{+196} \color{blue}{+189x} & = & \color{red}{-189x} +12 \color{blue}{+189x} \color{blue}{+196} \\\Leftrightarrow & -588x+189x& = & 12+196 \\\Leftrightarrow & \color{red}{-399} x& = & 208 \\\Leftrightarrow & x = \frac{208}{-399} & & \\\Leftrightarrow & x = \frac{-208}{399} & & \\ & V = \left\{ \frac{-208}{399} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{3}{5})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-84} & = & \color{red}{175x} +50 \\\Leftrightarrow & -420x \color{red}{-84} \color{blue}{+84} \color{blue}{-175x} & = & \color{red}{175x} +50 \color{blue}{-175x} \color{blue}{+84} \\\Leftrightarrow & -420x-175x& = & 50+84 \\\Leftrightarrow & \color{red}{-595} x& = & 134 \\\Leftrightarrow & x = \frac{134}{-595} & & \\\Leftrightarrow & x = \frac{-134}{595} & & \\ & V = \left\{ \frac{-134}{595} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{4}{7})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 24x-\frac{24}{7}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{168}{ \color{blue}{7} }x- \frac{24}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 168x \color{red}{-24} & = & \color{red}{-35x} +10 \\\Leftrightarrow & 168x \color{red}{-24} \color{blue}{+24} \color{blue}{+35x} & = & \color{red}{-35x} +10 \color{blue}{+35x} \color{blue}{+24} \\\Leftrightarrow & 168x+35x& = & 10+24 \\\Leftrightarrow & \color{red}{203} x& = & 34 \\\Leftrightarrow & x = \frac{34}{203} & & \\ & V = \left\{ \frac{34}{203} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{3}{5})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 8x+\frac{12}{5}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{+36} & = & \color{red}{75x} +10 \\\Leftrightarrow & 120x \color{red}{+36} \color{blue}{-36} \color{blue}{-75x} & = & \color{red}{75x} +10 \color{blue}{-75x} \color{blue}{-36} \\\Leftrightarrow & 120x-75x& = & 10-36 \\\Leftrightarrow & \color{red}{45} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{45} & & \\ & V = \left\{ \frac{-26}{45} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{3}{4})& = & 8x+\frac{2}{3} \\\Leftrightarrow & -15x+\frac{15}{4}& = & 8x+\frac{2}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-180}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -180x \color{red}{+45} & = & \color{red}{96x} +8 \\\Leftrightarrow & -180x \color{red}{+45} \color{blue}{-45} \color{blue}{-96x} & = & \color{red}{96x} +8 \color{blue}{-96x} \color{blue}{-45} \\\Leftrightarrow & -180x-96x& = & 8-45 \\\Leftrightarrow & \color{red}{-276} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-276} & & \\\Leftrightarrow & x = \frac{37}{276} & & \\ & V = \left\{ \frac{37}{276} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{3}{8})& = & 5x+\frac{7}{11} \\\Leftrightarrow & 28x-\frac{21}{8}& = & 5x+\frac{7}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{2464}{ \color{blue}{88} }x- \frac{231}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{56}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 2464x \color{red}{-231} & = & \color{red}{440x} +56 \\\Leftrightarrow & 2464x \color{red}{-231} \color{blue}{+231} \color{blue}{-440x} & = & \color{red}{440x} +56 \color{blue}{-440x} \color{blue}{+231} \\\Leftrightarrow & 2464x-440x& = & 56+231 \\\Leftrightarrow & \color{red}{2024} x& = & 287 \\\Leftrightarrow & x = \frac{287}{2024} & & \\ & V = \left\{ \frac{287}{2024} \right\} & \\\end{align}\)