Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{5}{9})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -6x-\frac{10}{9}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-54}{ \color{blue}{9} }x- \frac{10}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -54x \color{red}{-10} & = & \color{red}{-63x} +12 \\\Leftrightarrow & -54x \color{red}{-10} \color{blue}{+10} \color{blue}{+63x} & = & \color{red}{-63x} +12 \color{blue}{+63x} \color{blue}{+10} \\\Leftrightarrow & -54x+63x& = & 12+10 \\\Leftrightarrow & \color{red}{9} x& = & 22 \\\Leftrightarrow & x = \frac{22}{9} & & \\ & V = \left\{ \frac{22}{9} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{5}{11})& = & -7x+\frac{6}{7} \\\Leftrightarrow & -10x+\frac{10}{11}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{+70} & = & \color{red}{-539x} +66 \\\Leftrightarrow & -770x \color{red}{+70} \color{blue}{-70} \color{blue}{+539x} & = & \color{red}{-539x} +66 \color{blue}{+539x} \color{blue}{-70} \\\Leftrightarrow & -770x+539x& = & 66-70 \\\Leftrightarrow & \color{red}{-231} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-231} & & \\\Leftrightarrow & x = \frac{4}{231} & & \\ & V = \left\{ \frac{4}{231} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{2}{11})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 12x+\frac{6}{11}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+30} & = & \color{red}{275x} +66 \\\Leftrightarrow & 660x \color{red}{+30} \color{blue}{-30} \color{blue}{-275x} & = & \color{red}{275x} +66 \color{blue}{-275x} \color{blue}{-30} \\\Leftrightarrow & 660x-275x& = & 66-30 \\\Leftrightarrow & \color{red}{385} x& = & 36 \\\Leftrightarrow & x = \frac{36}{385} & & \\ & V = \left\{ \frac{36}{385} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{5}{7})& = & -5x+\frac{4}{5} \\\Leftrightarrow & 6x-\frac{15}{7}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{75}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-75} & = & \color{red}{-175x} +28 \\\Leftrightarrow & 210x \color{red}{-75} \color{blue}{+75} \color{blue}{+175x} & = & \color{red}{-175x} +28 \color{blue}{+175x} \color{blue}{+75} \\\Leftrightarrow & 210x+175x& = & 28+75 \\\Leftrightarrow & \color{red}{385} x& = & 103 \\\Leftrightarrow & x = \frac{103}{385} & & \\ & V = \left\{ \frac{103}{385} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{5}{6})& = & 3x+\frac{5}{7} \\\Leftrightarrow & 14x+\frac{35}{6}& = & 3x+\frac{5}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{588}{ \color{blue}{42} }x+ \frac{245}{ \color{blue}{42} })& = & (\frac{126}{ \color{blue}{42} }x+ \frac{30}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 588x \color{red}{+245} & = & \color{red}{126x} +30 \\\Leftrightarrow & 588x \color{red}{+245} \color{blue}{-245} \color{blue}{-126x} & = & \color{red}{126x} +30 \color{blue}{-126x} \color{blue}{-245} \\\Leftrightarrow & 588x-126x& = & 30-245 \\\Leftrightarrow & \color{red}{462} x& = & -215 \\\Leftrightarrow & x = \frac{-215}{462} & & \\ & V = \left\{ \frac{-215}{462} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{2}{9})& = & -7x+\frac{8}{9} \\\Leftrightarrow & -6x-\frac{4}{9}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-54}{ \color{blue}{9} }x- \frac{4}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -54x \color{red}{-4} & = & \color{red}{-63x} +8 \\\Leftrightarrow & -54x \color{red}{-4} \color{blue}{+4} \color{blue}{+63x} & = & \color{red}{-63x} +8 \color{blue}{+63x} \color{blue}{+4} \\\Leftrightarrow & -54x+63x& = & 8+4 \\\Leftrightarrow & \color{red}{9} x& = & 12 \\\Leftrightarrow & x = \frac{12}{9} & & \\\Leftrightarrow & x = \frac{4}{3} & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{5}{3})& = & -3x+\frac{5}{11} \\\Leftrightarrow & -8x+\frac{20}{3}& = & -3x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{+220} & = & \color{red}{-99x} +15 \\\Leftrightarrow & -264x \color{red}{+220} \color{blue}{-220} \color{blue}{+99x} & = & \color{red}{-99x} +15 \color{blue}{+99x} \color{blue}{-220} \\\Leftrightarrow & -264x+99x& = & 15-220 \\\Leftrightarrow & \color{red}{-165} x& = & -205 \\\Leftrightarrow & x = \frac{-205}{-165} & & \\\Leftrightarrow & x = \frac{41}{33} & & \\ & V = \left\{ \frac{41}{33} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{2}{9})& = & -3x+\frac{2}{11} \\\Leftrightarrow & 8x+\frac{8}{9}& = & -3x+\frac{2}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{792}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{18}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 792x \color{red}{+88} & = & \color{red}{-297x} +18 \\\Leftrightarrow & 792x \color{red}{+88} \color{blue}{-88} \color{blue}{+297x} & = & \color{red}{-297x} +18 \color{blue}{+297x} \color{blue}{-88} \\\Leftrightarrow & 792x+297x& = & 18-88 \\\Leftrightarrow & \color{red}{1089} x& = & -70 \\\Leftrightarrow & x = \frac{-70}{1089} & & \\ & V = \left\{ \frac{-70}{1089} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{4}{7})& = & 9x+\frac{7}{11} \\\Leftrightarrow & -20x+\frac{16}{7}& = & 9x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x+ \frac{176}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{+176} & = & \color{red}{693x} +49 \\\Leftrightarrow & -1540x \color{red}{+176} \color{blue}{-176} \color{blue}{-693x} & = & \color{red}{693x} +49 \color{blue}{-693x} \color{blue}{-176} \\\Leftrightarrow & -1540x-693x& = & 49-176 \\\Leftrightarrow & \color{red}{-2233} x& = & -127 \\\Leftrightarrow & x = \frac{-127}{-2233} & & \\\Leftrightarrow & x = \frac{127}{2233} & & \\ & V = \left\{ \frac{127}{2233} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{2}{7})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -10x-\frac{10}{7}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{-110} & = & \color{red}{539x} +70 \\\Leftrightarrow & -770x \color{red}{-110} \color{blue}{+110} \color{blue}{-539x} & = & \color{red}{539x} +70 \color{blue}{-539x} \color{blue}{+110} \\\Leftrightarrow & -770x-539x& = & 70+110 \\\Leftrightarrow & \color{red}{-1309} x& = & 180 \\\Leftrightarrow & x = \frac{180}{-1309} & & \\\Leftrightarrow & x = \frac{-180}{1309} & & \\ & V = \left\{ \frac{-180}{1309} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{3}{11})& = & -7x+\frac{9}{7} \\\Leftrightarrow & -20x-\frac{12}{11}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{-84} & = & \color{red}{-539x} +99 \\\Leftrightarrow & -1540x \color{red}{-84} \color{blue}{+84} \color{blue}{+539x} & = & \color{red}{-539x} +99 \color{blue}{+539x} \color{blue}{+84} \\\Leftrightarrow & -1540x+539x& = & 99+84 \\\Leftrightarrow & \color{red}{-1001} x& = & 183 \\\Leftrightarrow & x = \frac{183}{-1001} & & \\\Leftrightarrow & x = \frac{-183}{1001} & & \\ & V = \left\{ \frac{-183}{1001} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{3}{4})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -6x+\frac{9}{4}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-24}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} })& = & (\frac{-28}{ \color{blue}{4} }x+ \frac{18}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -24x \color{red}{+9} & = & \color{red}{-28x} +18 \\\Leftrightarrow & -24x \color{red}{+9} \color{blue}{-9} \color{blue}{+28x} & = & \color{red}{-28x} +18 \color{blue}{+28x} \color{blue}{-9} \\\Leftrightarrow & -24x+28x& = & 18-9 \\\Leftrightarrow & \color{red}{4} x& = & 9 \\\Leftrightarrow & x = \frac{9}{4} & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)