Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{2}{5})& = & -3x+\frac{2}{9} \\\Leftrightarrow & 20x+\frac{8}{5}& = & -3x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{900}{ \color{blue}{45} }x+ \frac{72}{ \color{blue}{45} })& = & (\frac{-135}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 900x \color{red}{+72} & = & \color{red}{-135x} +10 \\\Leftrightarrow & 900x \color{red}{+72} \color{blue}{-72} \color{blue}{+135x} & = & \color{red}{-135x} +10 \color{blue}{+135x} \color{blue}{-72} \\\Leftrightarrow & 900x+135x& = & 10-72 \\\Leftrightarrow & \color{red}{1035} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{1035} & & \\ & V = \left\{ \frac{-62}{1035} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{5}{3})& = & 9x+\frac{4}{5} \\\Leftrightarrow & -35x-\frac{35}{3}& = & 9x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-525}{ \color{blue}{15} }x- \frac{175}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -525x \color{red}{-175} & = & \color{red}{135x} +12 \\\Leftrightarrow & -525x \color{red}{-175} \color{blue}{+175} \color{blue}{-135x} & = & \color{red}{135x} +12 \color{blue}{-135x} \color{blue}{+175} \\\Leftrightarrow & -525x-135x& = & 12+175 \\\Leftrightarrow & \color{red}{-660} x& = & 187 \\\Leftrightarrow & x = \frac{187}{-660} & & \\\Leftrightarrow & x = \frac{-17}{60} & & \\ & V = \left\{ \frac{-17}{60} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{2}{5})& = & -7x+\frac{9}{11} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -7x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-132} & = & \color{red}{-385x} +45 \\\Leftrightarrow & 660x \color{red}{-132} \color{blue}{+132} \color{blue}{+385x} & = & \color{red}{-385x} +45 \color{blue}{+385x} \color{blue}{+132} \\\Leftrightarrow & 660x+385x& = & 45+132 \\\Leftrightarrow & \color{red}{1045} x& = & 177 \\\Leftrightarrow & x = \frac{177}{1045} & & \\ & V = \left\{ \frac{177}{1045} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{2}{3})& = & -6x+\frac{4}{3} \\\Leftrightarrow & 35x+\frac{14}{3}& = & -6x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{105}{ \color{blue}{3} }x+ \frac{14}{ \color{blue}{3} })& = & (\frac{-18}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 105x \color{red}{+14} & = & \color{red}{-18x} +4 \\\Leftrightarrow & 105x \color{red}{+14} \color{blue}{-14} \color{blue}{+18x} & = & \color{red}{-18x} +4 \color{blue}{+18x} \color{blue}{-14} \\\Leftrightarrow & 105x+18x& = & 4-14 \\\Leftrightarrow & \color{red}{123} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{123} & & \\ & V = \left\{ \frac{-10}{123} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{2}{11})& = & -7x+\frac{3}{8} \\\Leftrightarrow & 15x-\frac{10}{11}& = & -7x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1320}{ \color{blue}{88} }x- \frac{80}{ \color{blue}{88} })& = & (\frac{-616}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1320x \color{red}{-80} & = & \color{red}{-616x} +33 \\\Leftrightarrow & 1320x \color{red}{-80} \color{blue}{+80} \color{blue}{+616x} & = & \color{red}{-616x} +33 \color{blue}{+616x} \color{blue}{+80} \\\Leftrightarrow & 1320x+616x& = & 33+80 \\\Leftrightarrow & \color{red}{1936} x& = & 113 \\\Leftrightarrow & x = \frac{113}{1936} & & \\ & V = \left\{ \frac{113}{1936} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{2}{11})& = & 3x+\frac{6}{7} \\\Leftrightarrow & 8x+\frac{8}{11}& = & 3x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{+56} & = & \color{red}{231x} +66 \\\Leftrightarrow & 616x \color{red}{+56} \color{blue}{-56} \color{blue}{-231x} & = & \color{red}{231x} +66 \color{blue}{-231x} \color{blue}{-56} \\\Leftrightarrow & 616x-231x& = & 66-56 \\\Leftrightarrow & \color{red}{385} x& = & 10 \\\Leftrightarrow & x = \frac{10}{385} & & \\\Leftrightarrow & x = \frac{2}{77} & & \\ & V = \left\{ \frac{2}{77} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{3}{11})& = & -7x+\frac{3}{5} \\\Leftrightarrow & 30x-\frac{18}{11}& = & -7x+\frac{3}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x- \frac{90}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{33}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{-90} & = & \color{red}{-385x} +33 \\\Leftrightarrow & 1650x \color{red}{-90} \color{blue}{+90} \color{blue}{+385x} & = & \color{red}{-385x} +33 \color{blue}{+385x} \color{blue}{+90} \\\Leftrightarrow & 1650x+385x& = & 33+90 \\\Leftrightarrow & \color{red}{2035} x& = & 123 \\\Leftrightarrow & x = \frac{123}{2035} & & \\ & V = \left\{ \frac{123}{2035} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{2}{9})& = & -3x+\frac{4}{3} \\\Leftrightarrow & -14x-\frac{14}{9}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-126}{ \color{blue}{9} }x- \frac{14}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -126x \color{red}{-14} & = & \color{red}{-27x} +12 \\\Leftrightarrow & -126x \color{red}{-14} \color{blue}{+14} \color{blue}{+27x} & = & \color{red}{-27x} +12 \color{blue}{+27x} \color{blue}{+14} \\\Leftrightarrow & -126x+27x& = & 12+14 \\\Leftrightarrow & \color{red}{-99} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-99} & & \\\Leftrightarrow & x = \frac{-26}{99} & & \\ & V = \left\{ \frac{-26}{99} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{1}{3})& = & -3x+\frac{5}{2} \\\Leftrightarrow & 35x+\frac{7}{3}& = & -3x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{210}{ \color{blue}{6} }x+ \frac{14}{ \color{blue}{6} })& = & (\frac{-18}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 210x \color{red}{+14} & = & \color{red}{-18x} +15 \\\Leftrightarrow & 210x \color{red}{+14} \color{blue}{-14} \color{blue}{+18x} & = & \color{red}{-18x} +15 \color{blue}{+18x} \color{blue}{-14} \\\Leftrightarrow & 210x+18x& = & 15-14 \\\Leftrightarrow & \color{red}{228} x& = & 1 \\\Leftrightarrow & x = \frac{1}{228} & & \\ & V = \left\{ \frac{1}{228} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{2}{11})& = & 7x+\frac{7}{12} \\\Leftrightarrow & -10x+\frac{4}{11}& = & 7x+\frac{7}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-1320}{ \color{blue}{132} }x+ \frac{48}{ \color{blue}{132} })& = & (\frac{924}{ \color{blue}{132} }x+ \frac{77}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -1320x \color{red}{+48} & = & \color{red}{924x} +77 \\\Leftrightarrow & -1320x \color{red}{+48} \color{blue}{-48} \color{blue}{-924x} & = & \color{red}{924x} +77 \color{blue}{-924x} \color{blue}{-48} \\\Leftrightarrow & -1320x-924x& = & 77-48 \\\Leftrightarrow & \color{red}{-2244} x& = & 29 \\\Leftrightarrow & x = \frac{29}{-2244} & & \\\Leftrightarrow & x = \frac{-29}{2244} & & \\ & V = \left\{ \frac{-29}{2244} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{2}{5})& = & -3x+\frac{8}{11} \\\Leftrightarrow & 14x-\frac{14}{5}& = & -3x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{770}{ \color{blue}{55} }x- \frac{154}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 770x \color{red}{-154} & = & \color{red}{-165x} +40 \\\Leftrightarrow & 770x \color{red}{-154} \color{blue}{+154} \color{blue}{+165x} & = & \color{red}{-165x} +40 \color{blue}{+165x} \color{blue}{+154} \\\Leftrightarrow & 770x+165x& = & 40+154 \\\Leftrightarrow & \color{red}{935} x& = & 194 \\\Leftrightarrow & x = \frac{194}{935} & & \\ & V = \left\{ \frac{194}{935} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{4}{5})& = & -5x+\frac{2}{5} \\\Leftrightarrow & 6x+\frac{8}{5}& = & -5x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{30}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 30x \color{red}{+8} & = & \color{red}{-25x} +2 \\\Leftrightarrow & 30x \color{red}{+8} \color{blue}{-8} \color{blue}{+25x} & = & \color{red}{-25x} +2 \color{blue}{+25x} \color{blue}{-8} \\\Leftrightarrow & 30x+25x& = & 2-8 \\\Leftrightarrow & \color{red}{55} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{55} & & \\ & V = \left\{ \frac{-6}{55} \right\} & \\\end{align}\)