Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{4}{7})& = & -3x+\frac{2}{5} \\\Leftrightarrow & 20x-\frac{16}{7}& = & -3x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x- \frac{80}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{-80} & = & \color{red}{-105x} +14 \\\Leftrightarrow & 700x \color{red}{-80} \color{blue}{+80} \color{blue}{+105x} & = & \color{red}{-105x} +14 \color{blue}{+105x} \color{blue}{+80} \\\Leftrightarrow & 700x+105x& = & 14+80 \\\Leftrightarrow & \color{red}{805} x& = & 94 \\\Leftrightarrow & x = \frac{94}{805} & & \\ & V = \left\{ \frac{94}{805} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{4}{5})& = & 5x+\frac{3}{2} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{-24} & = & \color{red}{50x} +15 \\\Leftrightarrow & -120x \color{red}{-24} \color{blue}{+24} \color{blue}{-50x} & = & \color{red}{50x} +15 \color{blue}{-50x} \color{blue}{+24} \\\Leftrightarrow & -120x-50x& = & 15+24 \\\Leftrightarrow & \color{red}{-170} x& = & 39 \\\Leftrightarrow & x = \frac{39}{-170} & & \\\Leftrightarrow & x = \frac{-39}{170} & & \\ & V = \left\{ \frac{-39}{170} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{4}{3})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 10x-\frac{8}{3}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{30}{ \color{blue}{3} }x- \frac{8}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 30x \color{red}{-8} & = & \color{red}{21x} +2 \\\Leftrightarrow & 30x \color{red}{-8} \color{blue}{+8} \color{blue}{-21x} & = & \color{red}{21x} +2 \color{blue}{-21x} \color{blue}{+8} \\\Leftrightarrow & 30x-21x& = & 2+8 \\\Leftrightarrow & \color{red}{9} x& = & 10 \\\Leftrightarrow & x = \frac{10}{9} & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{4}{9})& = & -9x+\frac{5}{2} \\\Leftrightarrow & 14x-\frac{28}{9}& = & -9x+\frac{5}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{252}{ \color{blue}{18} }x- \frac{56}{ \color{blue}{18} })& = & (\frac{-162}{ \color{blue}{18} }x+ \frac{45}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 252x \color{red}{-56} & = & \color{red}{-162x} +45 \\\Leftrightarrow & 252x \color{red}{-56} \color{blue}{+56} \color{blue}{+162x} & = & \color{red}{-162x} +45 \color{blue}{+162x} \color{blue}{+56} \\\Leftrightarrow & 252x+162x& = & 45+56 \\\Leftrightarrow & \color{red}{414} x& = & 101 \\\Leftrightarrow & x = \frac{101}{414} & & \\ & V = \left\{ \frac{101}{414} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{4}{7})& = & 5x+\frac{5}{11} \\\Leftrightarrow & 8x-\frac{16}{7}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x- \frac{176}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{-176} & = & \color{red}{385x} +35 \\\Leftrightarrow & 616x \color{red}{-176} \color{blue}{+176} \color{blue}{-385x} & = & \color{red}{385x} +35 \color{blue}{-385x} \color{blue}{+176} \\\Leftrightarrow & 616x-385x& = & 35+176 \\\Leftrightarrow & \color{red}{231} x& = & 211 \\\Leftrightarrow & x = \frac{211}{231} & & \\ & V = \left\{ \frac{211}{231} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{3}{4})& = & -5x+\frac{3}{7} \\\Leftrightarrow & 12x+\frac{9}{4}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{336}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{12}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 336x \color{red}{+63} & = & \color{red}{-140x} +12 \\\Leftrightarrow & 336x \color{red}{+63} \color{blue}{-63} \color{blue}{+140x} & = & \color{red}{-140x} +12 \color{blue}{+140x} \color{blue}{-63} \\\Leftrightarrow & 336x+140x& = & 12-63 \\\Leftrightarrow & \color{red}{476} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{476} & & \\\Leftrightarrow & x = \frac{-3}{28} & & \\ & V = \left\{ \frac{-3}{28} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{4}{7})& = & 5x+\frac{7}{8} \\\Leftrightarrow & 6x-\frac{12}{7}& = & 5x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{336}{ \color{blue}{56} }x- \frac{96}{ \color{blue}{56} })& = & (\frac{280}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 336x \color{red}{-96} & = & \color{red}{280x} +49 \\\Leftrightarrow & 336x \color{red}{-96} \color{blue}{+96} \color{blue}{-280x} & = & \color{red}{280x} +49 \color{blue}{-280x} \color{blue}{+96} \\\Leftrightarrow & 336x-280x& = & 49+96 \\\Leftrightarrow & \color{red}{56} x& = & 145 \\\Leftrightarrow & x = \frac{145}{56} & & \\ & V = \left\{ \frac{145}{56} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{4}{11})& = & -9x+\frac{5}{4} \\\Leftrightarrow & -18x-\frac{24}{11}& = & -9x+\frac{5}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-792}{ \color{blue}{44} }x- \frac{96}{ \color{blue}{44} })& = & (\frac{-396}{ \color{blue}{44} }x+ \frac{55}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -792x \color{red}{-96} & = & \color{red}{-396x} +55 \\\Leftrightarrow & -792x \color{red}{-96} \color{blue}{+96} \color{blue}{+396x} & = & \color{red}{-396x} +55 \color{blue}{+396x} \color{blue}{+96} \\\Leftrightarrow & -792x+396x& = & 55+96 \\\Leftrightarrow & \color{red}{-396} x& = & 151 \\\Leftrightarrow & x = \frac{151}{-396} & & \\\Leftrightarrow & x = \frac{-151}{396} & & \\ & V = \left\{ \frac{-151}{396} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{4}{3})& = & 7x+\frac{5}{4} \\\Leftrightarrow & 20x-\frac{20}{3}& = & 7x+\frac{5}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{240}{ \color{blue}{12} }x- \frac{80}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{15}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 240x \color{red}{-80} & = & \color{red}{84x} +15 \\\Leftrightarrow & 240x \color{red}{-80} \color{blue}{+80} \color{blue}{-84x} & = & \color{red}{84x} +15 \color{blue}{-84x} \color{blue}{+80} \\\Leftrightarrow & 240x-84x& = & 15+80 \\\Leftrightarrow & \color{red}{156} x& = & 95 \\\Leftrightarrow & x = \frac{95}{156} & & \\ & V = \left\{ \frac{95}{156} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{2}{11})& = & 9x+\frac{8}{3} \\\Leftrightarrow & -25x-\frac{10}{11}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-825}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -825x \color{red}{-30} & = & \color{red}{297x} +88 \\\Leftrightarrow & -825x \color{red}{-30} \color{blue}{+30} \color{blue}{-297x} & = & \color{red}{297x} +88 \color{blue}{-297x} \color{blue}{+30} \\\Leftrightarrow & -825x-297x& = & 88+30 \\\Leftrightarrow & \color{red}{-1122} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-1122} & & \\\Leftrightarrow & x = \frac{-59}{561} & & \\ & V = \left\{ \frac{-59}{561} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{2}{7})& = & -4x+\frac{2}{11} \\\Leftrightarrow & -15x+\frac{10}{7}& = & -4x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{-308}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{+110} & = & \color{red}{-308x} +14 \\\Leftrightarrow & -1155x \color{red}{+110} \color{blue}{-110} \color{blue}{+308x} & = & \color{red}{-308x} +14 \color{blue}{+308x} \color{blue}{-110} \\\Leftrightarrow & -1155x+308x& = & 14-110 \\\Leftrightarrow & \color{red}{-847} x& = & -96 \\\Leftrightarrow & x = \frac{-96}{-847} & & \\\Leftrightarrow & x = \frac{96}{847} & & \\ & V = \left\{ \frac{96}{847} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{3})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -6x-\frac{8}{3}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{-40} & = & \color{red}{-105x} +18 \\\Leftrightarrow & -90x \color{red}{-40} \color{blue}{+40} \color{blue}{+105x} & = & \color{red}{-105x} +18 \color{blue}{+105x} \color{blue}{+40} \\\Leftrightarrow & -90x+105x& = & 18+40 \\\Leftrightarrow & \color{red}{15} x& = & 58 \\\Leftrightarrow & x = \frac{58}{15} & & \\ & V = \left\{ \frac{58}{15} \right\} & \\\end{align}\)