Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{5}{7})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -12x+\frac{30}{7}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{+30} & = & \color{red}{-35x} +2 \\\Leftrightarrow & -84x \color{red}{+30} \color{blue}{-30} \color{blue}{+35x} & = & \color{red}{-35x} +2 \color{blue}{+35x} \color{blue}{-30} \\\Leftrightarrow & -84x+35x& = & 2-30 \\\Leftrightarrow & \color{red}{-49} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{-49} & & \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{5}{7})& = & -7x+\frac{8}{7} \\\Leftrightarrow & 12x+\frac{30}{7}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{+30} & = & \color{red}{-49x} +8 \\\Leftrightarrow & 84x \color{red}{+30} \color{blue}{-30} \color{blue}{+49x} & = & \color{red}{-49x} +8 \color{blue}{+49x} \color{blue}{-30} \\\Leftrightarrow & 84x+49x& = & 8-30 \\\Leftrightarrow & \color{red}{133} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{133} & & \\ & V = \left\{ \frac{-22}{133} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{4}{11})& = & 5x+\frac{3}{8} \\\Leftrightarrow & -24x-\frac{24}{11}& = & 5x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2112}{ \color{blue}{88} }x- \frac{192}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2112x \color{red}{-192} & = & \color{red}{440x} +33 \\\Leftrightarrow & -2112x \color{red}{-192} \color{blue}{+192} \color{blue}{-440x} & = & \color{red}{440x} +33 \color{blue}{-440x} \color{blue}{+192} \\\Leftrightarrow & -2112x-440x& = & 33+192 \\\Leftrightarrow & \color{red}{-2552} x& = & 225 \\\Leftrightarrow & x = \frac{225}{-2552} & & \\\Leftrightarrow & x = \frac{-225}{2552} & & \\ & V = \left\{ \frac{-225}{2552} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{7})& = & 7x+\frac{7}{8} \\\Leftrightarrow & -30x-\frac{30}{7}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1680}{ \color{blue}{56} }x- \frac{240}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1680x \color{red}{-240} & = & \color{red}{392x} +49 \\\Leftrightarrow & -1680x \color{red}{-240} \color{blue}{+240} \color{blue}{-392x} & = & \color{red}{392x} +49 \color{blue}{-392x} \color{blue}{+240} \\\Leftrightarrow & -1680x-392x& = & 49+240 \\\Leftrightarrow & \color{red}{-2072} x& = & 289 \\\Leftrightarrow & x = \frac{289}{-2072} & & \\\Leftrightarrow & x = \frac{-289}{2072} & & \\ & V = \left\{ \frac{-289}{2072} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{4}{5})& = & 9x+\frac{10}{7} \\\Leftrightarrow & -18x-\frac{24}{5}& = & 9x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x- \frac{168}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{-168} & = & \color{red}{315x} +50 \\\Leftrightarrow & -630x \color{red}{-168} \color{blue}{+168} \color{blue}{-315x} & = & \color{red}{315x} +50 \color{blue}{-315x} \color{blue}{+168} \\\Leftrightarrow & -630x-315x& = & 50+168 \\\Leftrightarrow & \color{red}{-945} x& = & 218 \\\Leftrightarrow & x = \frac{218}{-945} & & \\\Leftrightarrow & x = \frac{-218}{945} & & \\ & V = \left\{ \frac{-218}{945} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{4}{7})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 6x-\frac{8}{7}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x- \frac{24}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{-24} & = & \color{red}{105x} +70 \\\Leftrightarrow & 126x \color{red}{-24} \color{blue}{+24} \color{blue}{-105x} & = & \color{red}{105x} +70 \color{blue}{-105x} \color{blue}{+24} \\\Leftrightarrow & 126x-105x& = & 70+24 \\\Leftrightarrow & \color{red}{21} x& = & 94 \\\Leftrightarrow & x = \frac{94}{21} & & \\ & V = \left\{ \frac{94}{21} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{8})& = & -7x+\frac{3}{7} \\\Leftrightarrow & -10x-\frac{15}{8}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-560}{ \color{blue}{56} }x- \frac{105}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{24}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -560x \color{red}{-105} & = & \color{red}{-392x} +24 \\\Leftrightarrow & -560x \color{red}{-105} \color{blue}{+105} \color{blue}{+392x} & = & \color{red}{-392x} +24 \color{blue}{+392x} \color{blue}{+105} \\\Leftrightarrow & -560x+392x& = & 24+105 \\\Leftrightarrow & \color{red}{-168} x& = & 129 \\\Leftrightarrow & x = \frac{129}{-168} & & \\\Leftrightarrow & x = \frac{-43}{56} & & \\ & V = \left\{ \frac{-43}{56} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{5}{7})& = & 7x+\frac{9}{10} \\\Leftrightarrow & 30x-\frac{30}{7}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{2100}{ \color{blue}{70} }x- \frac{300}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 2100x \color{red}{-300} & = & \color{red}{490x} +63 \\\Leftrightarrow & 2100x \color{red}{-300} \color{blue}{+300} \color{blue}{-490x} & = & \color{red}{490x} +63 \color{blue}{-490x} \color{blue}{+300} \\\Leftrightarrow & 2100x-490x& = & 63+300 \\\Leftrightarrow & \color{red}{1610} x& = & 363 \\\Leftrightarrow & x = \frac{363}{1610} & & \\ & V = \left\{ \frac{363}{1610} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{3}{4})& = & 7x+\frac{4}{9} \\\Leftrightarrow & -20x+\frac{15}{4}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-720}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{252}{ \color{blue}{36} }x+ \frac{16}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -720x \color{red}{+135} & = & \color{red}{252x} +16 \\\Leftrightarrow & -720x \color{red}{+135} \color{blue}{-135} \color{blue}{-252x} & = & \color{red}{252x} +16 \color{blue}{-252x} \color{blue}{-135} \\\Leftrightarrow & -720x-252x& = & 16-135 \\\Leftrightarrow & \color{red}{-972} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{-972} & & \\\Leftrightarrow & x = \frac{119}{972} & & \\ & V = \left\{ \frac{119}{972} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{2}{11})& = & 9x+\frac{2}{3} \\\Leftrightarrow & 28x+\frac{14}{11}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{924}{ \color{blue}{33} }x+ \frac{42}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 924x \color{red}{+42} & = & \color{red}{297x} +22 \\\Leftrightarrow & 924x \color{red}{+42} \color{blue}{-42} \color{blue}{-297x} & = & \color{red}{297x} +22 \color{blue}{-297x} \color{blue}{-42} \\\Leftrightarrow & 924x-297x& = & 22-42 \\\Leftrightarrow & \color{red}{627} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{627} & & \\ & V = \left\{ \frac{-20}{627} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{3}{7})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -6x+\frac{6}{7}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+66} & = & \color{red}{-539x} +42 \\\Leftrightarrow & -462x \color{red}{+66} \color{blue}{-66} \color{blue}{+539x} & = & \color{red}{-539x} +42 \color{blue}{+539x} \color{blue}{-66} \\\Leftrightarrow & -462x+539x& = & 42-66 \\\Leftrightarrow & \color{red}{77} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{77} & & \\ & V = \left\{ \frac{-24}{77} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{5}{11})& = & 7x+\frac{3}{7} \\\Leftrightarrow & -6x+\frac{15}{11}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{105}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+105} & = & \color{red}{539x} +33 \\\Leftrightarrow & -462x \color{red}{+105} \color{blue}{-105} \color{blue}{-539x} & = & \color{red}{539x} +33 \color{blue}{-539x} \color{blue}{-105} \\\Leftrightarrow & -462x-539x& = & 33-105 \\\Leftrightarrow & \color{red}{-1001} x& = & -72 \\\Leftrightarrow & x = \frac{-72}{-1001} & & \\\Leftrightarrow & x = \frac{72}{1001} & & \\ & V = \left\{ \frac{72}{1001} \right\} & \\\end{align}\)