Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{4}{5})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 18x+\frac{24}{5}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{+264} & = & \color{red}{275x} +30 \\\Leftrightarrow & 990x \color{red}{+264} \color{blue}{-264} \color{blue}{-275x} & = & \color{red}{275x} +30 \color{blue}{-275x} \color{blue}{-264} \\\Leftrightarrow & 990x-275x& = & 30-264 \\\Leftrightarrow & \color{red}{715} x& = & -234 \\\Leftrightarrow & x = \frac{-234}{715} & & \\\Leftrightarrow & x = \frac{-18}{55} & & \\ & V = \left\{ \frac{-18}{55} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{5}{6})& = & -9x+\frac{3}{2} \\\Leftrightarrow & 14x+\frac{35}{6}& = & -9x+\frac{3}{2} \\ & & & \text{kgv van noemers 6 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{84}{ \color{blue}{6} }x+ \frac{35}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 84x \color{red}{+35} & = & \color{red}{-54x} +9 \\\Leftrightarrow & 84x \color{red}{+35} \color{blue}{-35} \color{blue}{+54x} & = & \color{red}{-54x} +9 \color{blue}{+54x} \color{blue}{-35} \\\Leftrightarrow & 84x+54x& = & 9-35 \\\Leftrightarrow & \color{red}{138} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{138} & & \\\Leftrightarrow & x = \frac{-13}{69} & & \\ & V = \left\{ \frac{-13}{69} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{2})& = & 9x+\frac{10}{3} \\\Leftrightarrow & 10x-\frac{25}{2}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{60}{ \color{blue}{6} }x- \frac{75}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 60x \color{red}{-75} & = & \color{red}{54x} +20 \\\Leftrightarrow & 60x \color{red}{-75} \color{blue}{+75} \color{blue}{-54x} & = & \color{red}{54x} +20 \color{blue}{-54x} \color{blue}{+75} \\\Leftrightarrow & 60x-54x& = & 20+75 \\\Leftrightarrow & \color{red}{6} x& = & 95 \\\Leftrightarrow & x = \frac{95}{6} & & \\ & V = \left\{ \frac{95}{6} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{5}{7})& = & 7x+\frac{9}{10} \\\Leftrightarrow & -30x+\frac{30}{7}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-2100}{ \color{blue}{70} }x+ \frac{300}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -2100x \color{red}{+300} & = & \color{red}{490x} +63 \\\Leftrightarrow & -2100x \color{red}{+300} \color{blue}{-300} \color{blue}{-490x} & = & \color{red}{490x} +63 \color{blue}{-490x} \color{blue}{-300} \\\Leftrightarrow & -2100x-490x& = & 63-300 \\\Leftrightarrow & \color{red}{-2590} x& = & -237 \\\Leftrightarrow & x = \frac{-237}{-2590} & & \\\Leftrightarrow & x = \frac{237}{2590} & & \\ & V = \left\{ \frac{237}{2590} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{4}{3})& = & 7x+\frac{7}{9} \\\Leftrightarrow & -10x-\frac{20}{3}& = & 7x+\frac{7}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x- \frac{60}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{-60} & = & \color{red}{63x} +7 \\\Leftrightarrow & -90x \color{red}{-60} \color{blue}{+60} \color{blue}{-63x} & = & \color{red}{63x} +7 \color{blue}{-63x} \color{blue}{+60} \\\Leftrightarrow & -90x-63x& = & 7+60 \\\Leftrightarrow & \color{red}{-153} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-153} & & \\\Leftrightarrow & x = \frac{-67}{153} & & \\ & V = \left\{ \frac{-67}{153} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{3}{4})& = & 6x+\frac{4}{9} \\\Leftrightarrow & 25x-\frac{15}{4}& = & 6x+\frac{4}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{900}{ \color{blue}{36} }x- \frac{135}{ \color{blue}{36} })& = & (\frac{216}{ \color{blue}{36} }x+ \frac{16}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 900x \color{red}{-135} & = & \color{red}{216x} +16 \\\Leftrightarrow & 900x \color{red}{-135} \color{blue}{+135} \color{blue}{-216x} & = & \color{red}{216x} +16 \color{blue}{-216x} \color{blue}{+135} \\\Leftrightarrow & 900x-216x& = & 16+135 \\\Leftrightarrow & \color{red}{684} x& = & 151 \\\Leftrightarrow & x = \frac{151}{684} & & \\ & V = \left\{ \frac{151}{684} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{4}{3})& = & 9x+\frac{4}{3} \\\Leftrightarrow & -8x-\frac{16}{3}& = & 9x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-24}{ \color{blue}{3} }x- \frac{16}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -24x \color{red}{-16} & = & \color{red}{27x} +4 \\\Leftrightarrow & -24x \color{red}{-16} \color{blue}{+16} \color{blue}{-27x} & = & \color{red}{27x} +4 \color{blue}{-27x} \color{blue}{+16} \\\Leftrightarrow & -24x-27x& = & 4+16 \\\Leftrightarrow & \color{red}{-51} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-51} & & \\\Leftrightarrow & x = \frac{-20}{51} & & \\ & V = \left\{ \frac{-20}{51} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{2}{5})& = & -7x+\frac{2}{11} \\\Leftrightarrow & 30x+\frac{12}{5}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{+132} & = & \color{red}{-385x} +10 \\\Leftrightarrow & 1650x \color{red}{+132} \color{blue}{-132} \color{blue}{+385x} & = & \color{red}{-385x} +10 \color{blue}{+385x} \color{blue}{-132} \\\Leftrightarrow & 1650x+385x& = & 10-132 \\\Leftrightarrow & \color{red}{2035} x& = & -122 \\\Leftrightarrow & x = \frac{-122}{2035} & & \\ & V = \left\{ \frac{-122}{2035} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{1}{2})& = & 7x+\frac{3}{10} \\\Leftrightarrow & -10x+\frac{5}{2}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 2 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-100}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -100x \color{red}{+25} & = & \color{red}{70x} +3 \\\Leftrightarrow & -100x \color{red}{+25} \color{blue}{-25} \color{blue}{-70x} & = & \color{red}{70x} +3 \color{blue}{-70x} \color{blue}{-25} \\\Leftrightarrow & -100x-70x& = & 3-25 \\\Leftrightarrow & \color{red}{-170} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-170} & & \\\Leftrightarrow & x = \frac{11}{85} & & \\ & V = \left\{ \frac{11}{85} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{4}{11})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -30x+\frac{24}{11}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-330}{ \color{blue}{11} }x+ \frac{24}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -330x \color{red}{+24} & = & \color{red}{-77x} +6 \\\Leftrightarrow & -330x \color{red}{+24} \color{blue}{-24} \color{blue}{+77x} & = & \color{red}{-77x} +6 \color{blue}{+77x} \color{blue}{-24} \\\Leftrightarrow & -330x+77x& = & 6-24 \\\Leftrightarrow & \color{red}{-253} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-253} & & \\\Leftrightarrow & x = \frac{18}{253} & & \\ & V = \left\{ \frac{18}{253} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{5}{12})& = & -3x+\frac{4}{7} \\\Leftrightarrow & 10x-\frac{25}{12}& = & -3x+\frac{4}{7} \\ & & & \text{kgv van noemers 12 en 7 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{840}{ \color{blue}{84} }x- \frac{175}{ \color{blue}{84} })& = & (\frac{-252}{ \color{blue}{84} }x+ \frac{48}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 840x \color{red}{-175} & = & \color{red}{-252x} +48 \\\Leftrightarrow & 840x \color{red}{-175} \color{blue}{+175} \color{blue}{+252x} & = & \color{red}{-252x} +48 \color{blue}{+252x} \color{blue}{+175} \\\Leftrightarrow & 840x+252x& = & 48+175 \\\Leftrightarrow & \color{red}{1092} x& = & 223 \\\Leftrightarrow & x = \frac{223}{1092} & & \\ & V = \left\{ \frac{223}{1092} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{5}{4})& = & -7x+\frac{8}{5} \\\Leftrightarrow & 12x+\frac{15}{4}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{240}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{32}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 240x \color{red}{+75} & = & \color{red}{-140x} +32 \\\Leftrightarrow & 240x \color{red}{+75} \color{blue}{-75} \color{blue}{+140x} & = & \color{red}{-140x} +32 \color{blue}{+140x} \color{blue}{-75} \\\Leftrightarrow & 240x+140x& = & 32-75 \\\Leftrightarrow & \color{red}{380} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{380} & & \\ & V = \left\{ \frac{-43}{380} \right\} & \\\end{align}\)