Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{2}{5})& = & -7x+\frac{7}{5} \\\Leftrightarrow & -30x-\frac{12}{5}& = & -7x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-150}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -150x \color{red}{-12} & = & \color{red}{-35x} +7 \\\Leftrightarrow & -150x \color{red}{-12} \color{blue}{+12} \color{blue}{+35x} & = & \color{red}{-35x} +7 \color{blue}{+35x} \color{blue}{+12} \\\Leftrightarrow & -150x+35x& = & 7+12 \\\Leftrightarrow & \color{red}{-115} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-115} & & \\\Leftrightarrow & x = \frac{-19}{115} & & \\ & V = \left\{ \frac{-19}{115} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{2}{7})& = & 7x+\frac{8}{11} \\\Leftrightarrow & -25x+\frac{10}{7}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1925}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1925x \color{red}{+110} & = & \color{red}{539x} +56 \\\Leftrightarrow & -1925x \color{red}{+110} \color{blue}{-110} \color{blue}{-539x} & = & \color{red}{539x} +56 \color{blue}{-539x} \color{blue}{-110} \\\Leftrightarrow & -1925x-539x& = & 56-110 \\\Leftrightarrow & \color{red}{-2464} x& = & -54 \\\Leftrightarrow & x = \frac{-54}{-2464} & & \\\Leftrightarrow & x = \frac{27}{1232} & & \\ & V = \left\{ \frac{27}{1232} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{2}{3})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 12x-\frac{8}{3}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{72}{ \color{blue}{6} }x- \frac{16}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 72x \color{red}{-16} & = & \color{red}{-42x} +9 \\\Leftrightarrow & 72x \color{red}{-16} \color{blue}{+16} \color{blue}{+42x} & = & \color{red}{-42x} +9 \color{blue}{+42x} \color{blue}{+16} \\\Leftrightarrow & 72x+42x& = & 9+16 \\\Leftrightarrow & \color{red}{114} x& = & 25 \\\Leftrightarrow & x = \frac{25}{114} & & \\ & V = \left\{ \frac{25}{114} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{5}{11})& = & -7x+\frac{3}{11} \\\Leftrightarrow & 10x-\frac{10}{11}& = & -7x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{110}{ \color{blue}{11} }x- \frac{10}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 110x \color{red}{-10} & = & \color{red}{-77x} +3 \\\Leftrightarrow & 110x \color{red}{-10} \color{blue}{+10} \color{blue}{+77x} & = & \color{red}{-77x} +3 \color{blue}{+77x} \color{blue}{+10} \\\Leftrightarrow & 110x+77x& = & 3+10 \\\Leftrightarrow & \color{red}{187} x& = & 13 \\\Leftrightarrow & x = \frac{13}{187} & & \\ & V = \left\{ \frac{13}{187} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{2}{3})& = & 9x+\frac{7}{6} \\\Leftrightarrow & -35x-\frac{14}{3}& = & 9x+\frac{7}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-210}{ \color{blue}{6} }x- \frac{28}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{7}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -210x \color{red}{-28} & = & \color{red}{54x} +7 \\\Leftrightarrow & -210x \color{red}{-28} \color{blue}{+28} \color{blue}{-54x} & = & \color{red}{54x} +7 \color{blue}{-54x} \color{blue}{+28} \\\Leftrightarrow & -210x-54x& = & 7+28 \\\Leftrightarrow & \color{red}{-264} x& = & 35 \\\Leftrightarrow & x = \frac{35}{-264} & & \\\Leftrightarrow & x = \frac{-35}{264} & & \\ & V = \left\{ \frac{-35}{264} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{5}{7})& = & 3x+\frac{3}{11} \\\Leftrightarrow & 10x+\frac{25}{7}& = & 3x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x+ \frac{275}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{+275} & = & \color{red}{231x} +21 \\\Leftrightarrow & 770x \color{red}{+275} \color{blue}{-275} \color{blue}{-231x} & = & \color{red}{231x} +21 \color{blue}{-231x} \color{blue}{-275} \\\Leftrightarrow & 770x-231x& = & 21-275 \\\Leftrightarrow & \color{red}{539} x& = & -254 \\\Leftrightarrow & x = \frac{-254}{539} & & \\ & V = \left\{ \frac{-254}{539} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{4}{5})& = & 7x+\frac{5}{11} \\\Leftrightarrow & 30x-\frac{24}{5}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x- \frac{264}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{-264} & = & \color{red}{385x} +25 \\\Leftrightarrow & 1650x \color{red}{-264} \color{blue}{+264} \color{blue}{-385x} & = & \color{red}{385x} +25 \color{blue}{-385x} \color{blue}{+264} \\\Leftrightarrow & 1650x-385x& = & 25+264 \\\Leftrightarrow & \color{red}{1265} x& = & 289 \\\Leftrightarrow & x = \frac{289}{1265} & & \\ & V = \left\{ \frac{289}{1265} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{4}{7})& = & -7x+\frac{4}{7} \\\Leftrightarrow & 18x+\frac{24}{7}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{126}{ \color{blue}{7} }x+ \frac{24}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 126x \color{red}{+24} & = & \color{red}{-49x} +4 \\\Leftrightarrow & 126x \color{red}{+24} \color{blue}{-24} \color{blue}{+49x} & = & \color{red}{-49x} +4 \color{blue}{+49x} \color{blue}{-24} \\\Leftrightarrow & 126x+49x& = & 4-24 \\\Leftrightarrow & \color{red}{175} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{175} & & \\\Leftrightarrow & x = \frac{-4}{35} & & \\ & V = \left\{ \frac{-4}{35} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{2}{11})& = & -3x+\frac{7}{2} \\\Leftrightarrow & -8x+\frac{4}{11}& = & -3x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-176}{ \color{blue}{22} }x+ \frac{8}{ \color{blue}{22} })& = & (\frac{-66}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -176x \color{red}{+8} & = & \color{red}{-66x} +77 \\\Leftrightarrow & -176x \color{red}{+8} \color{blue}{-8} \color{blue}{+66x} & = & \color{red}{-66x} +77 \color{blue}{+66x} \color{blue}{-8} \\\Leftrightarrow & -176x+66x& = & 77-8 \\\Leftrightarrow & \color{red}{-110} x& = & 69 \\\Leftrightarrow & x = \frac{69}{-110} & & \\\Leftrightarrow & x = \frac{-69}{110} & & \\ & V = \left\{ \frac{-69}{110} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{2}{3})& = & -3x+\frac{2}{11} \\\Leftrightarrow & -8x+\frac{4}{3}& = & -3x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{+44} & = & \color{red}{-99x} +6 \\\Leftrightarrow & -264x \color{red}{+44} \color{blue}{-44} \color{blue}{+99x} & = & \color{red}{-99x} +6 \color{blue}{+99x} \color{blue}{-44} \\\Leftrightarrow & -264x+99x& = & 6-44 \\\Leftrightarrow & \color{red}{-165} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{-165} & & \\\Leftrightarrow & x = \frac{38}{165} & & \\ & V = \left\{ \frac{38}{165} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{3}{5})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -12x-\frac{18}{5}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{198}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-198} & = & \color{red}{-275x} +30 \\\Leftrightarrow & -660x \color{red}{-198} \color{blue}{+198} \color{blue}{+275x} & = & \color{red}{-275x} +30 \color{blue}{+275x} \color{blue}{+198} \\\Leftrightarrow & -660x+275x& = & 30+198 \\\Leftrightarrow & \color{red}{-385} x& = & 228 \\\Leftrightarrow & x = \frac{228}{-385} & & \\\Leftrightarrow & x = \frac{-228}{385} & & \\ & V = \left\{ \frac{-228}{385} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{2}{7})& = & 5x+\frac{4}{5} \\\Leftrightarrow & 12x+\frac{6}{7}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+30} & = & \color{red}{175x} +28 \\\Leftrightarrow & 420x \color{red}{+30} \color{blue}{-30} \color{blue}{-175x} & = & \color{red}{175x} +28 \color{blue}{-175x} \color{blue}{-30} \\\Leftrightarrow & 420x-175x& = & 28-30 \\\Leftrightarrow & \color{red}{245} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{245} & & \\ & V = \left\{ \frac{-2}{245} \right\} & \\\end{align}\)