Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{3}{8})& = & 3x+\frac{2}{5} \\\Leftrightarrow & -35x-\frac{21}{8}& = & 3x+\frac{2}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1400}{ \color{blue}{40} }x- \frac{105}{ \color{blue}{40} })& = & (\frac{120}{ \color{blue}{40} }x+ \frac{16}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1400x \color{red}{-105} & = & \color{red}{120x} +16 \\\Leftrightarrow & -1400x \color{red}{-105} \color{blue}{+105} \color{blue}{-120x} & = & \color{red}{120x} +16 \color{blue}{-120x} \color{blue}{+105} \\\Leftrightarrow & -1400x-120x& = & 16+105 \\\Leftrightarrow & \color{red}{-1520} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-1520} & & \\\Leftrightarrow & x = \frac{-121}{1520} & & \\ & V = \left\{ \frac{-121}{1520} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{3}{11})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -16x+\frac{12}{11}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-880}{ \color{blue}{55} }x+ \frac{60}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -880x \color{red}{+60} & = & \color{red}{385x} +66 \\\Leftrightarrow & -880x \color{red}{+60} \color{blue}{-60} \color{blue}{-385x} & = & \color{red}{385x} +66 \color{blue}{-385x} \color{blue}{-60} \\\Leftrightarrow & -880x-385x& = & 66-60 \\\Leftrightarrow & \color{red}{-1265} x& = & 6 \\\Leftrightarrow & x = \frac{6}{-1265} & & \\\Leftrightarrow & x = \frac{-6}{1265} & & \\ & V = \left\{ \frac{-6}{1265} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{2}{11})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 16x+\frac{8}{11}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{352}{ \color{blue}{22} }x+ \frac{16}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 352x \color{red}{+16} & = & \color{red}{-154x} +33 \\\Leftrightarrow & 352x \color{red}{+16} \color{blue}{-16} \color{blue}{+154x} & = & \color{red}{-154x} +33 \color{blue}{+154x} \color{blue}{-16} \\\Leftrightarrow & 352x+154x& = & 33-16 \\\Leftrightarrow & \color{red}{506} x& = & 17 \\\Leftrightarrow & x = \frac{17}{506} & & \\ & V = \left\{ \frac{17}{506} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{3}{11})& = & 9x+\frac{2}{7} \\\Leftrightarrow & 4x+\frac{6}{11}& = & 9x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{308}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 308x \color{red}{+42} & = & \color{red}{693x} +22 \\\Leftrightarrow & 308x \color{red}{+42} \color{blue}{-42} \color{blue}{-693x} & = & \color{red}{693x} +22 \color{blue}{-693x} \color{blue}{-42} \\\Leftrightarrow & 308x-693x& = & 22-42 \\\Leftrightarrow & \color{red}{-385} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-385} & & \\\Leftrightarrow & x = \frac{4}{77} & & \\ & V = \left\{ \frac{4}{77} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{4}{5})& = & 5x+\frac{8}{5} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{-12} & = & \color{red}{25x} +8 \\\Leftrightarrow & -60x \color{red}{-12} \color{blue}{+12} \color{blue}{-25x} & = & \color{red}{25x} +8 \color{blue}{-25x} \color{blue}{+12} \\\Leftrightarrow & -60x-25x& = & 8+12 \\\Leftrightarrow & \color{red}{-85} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-85} & & \\\Leftrightarrow & x = \frac{-4}{17} & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{3}{8})& = & -2x+\frac{3}{2} \\\Leftrightarrow & 21x+\frac{21}{8}& = & -2x+\frac{3}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{168}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{-16}{ \color{blue}{8} }x+ \frac{12}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 168x \color{red}{+21} & = & \color{red}{-16x} +12 \\\Leftrightarrow & 168x \color{red}{+21} \color{blue}{-21} \color{blue}{+16x} & = & \color{red}{-16x} +12 \color{blue}{+16x} \color{blue}{-21} \\\Leftrightarrow & 168x+16x& = & 12-21 \\\Leftrightarrow & \color{red}{184} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{184} & & \\ & V = \left\{ \frac{-9}{184} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{3}{11})& = & 7x+\frac{7}{4} \\\Leftrightarrow & -30x+\frac{18}{11}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1320}{ \color{blue}{44} }x+ \frac{72}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{77}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1320x \color{red}{+72} & = & \color{red}{308x} +77 \\\Leftrightarrow & -1320x \color{red}{+72} \color{blue}{-72} \color{blue}{-308x} & = & \color{red}{308x} +77 \color{blue}{-308x} \color{blue}{-72} \\\Leftrightarrow & -1320x-308x& = & 77-72 \\\Leftrightarrow & \color{red}{-1628} x& = & 5 \\\Leftrightarrow & x = \frac{5}{-1628} & & \\\Leftrightarrow & x = \frac{-5}{1628} & & \\ & V = \left\{ \frac{-5}{1628} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{5}{11})& = & 7x+\frac{8}{5} \\\Leftrightarrow & -6x-\frac{15}{11}& = & 7x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x- \frac{75}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{-75} & = & \color{red}{385x} +88 \\\Leftrightarrow & -330x \color{red}{-75} \color{blue}{+75} \color{blue}{-385x} & = & \color{red}{385x} +88 \color{blue}{-385x} \color{blue}{+75} \\\Leftrightarrow & -330x-385x& = & 88+75 \\\Leftrightarrow & \color{red}{-715} x& = & 163 \\\Leftrightarrow & x = \frac{163}{-715} & & \\\Leftrightarrow & x = \frac{-163}{715} & & \\ & V = \left\{ \frac{-163}{715} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{2}{5})& = & -7x+\frac{8}{11} \\\Leftrightarrow & 18x-\frac{12}{5}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{-132} & = & \color{red}{-385x} +40 \\\Leftrightarrow & 990x \color{red}{-132} \color{blue}{+132} \color{blue}{+385x} & = & \color{red}{-385x} +40 \color{blue}{+385x} \color{blue}{+132} \\\Leftrightarrow & 990x+385x& = & 40+132 \\\Leftrightarrow & \color{red}{1375} x& = & 172 \\\Leftrightarrow & x = \frac{172}{1375} & & \\ & V = \left\{ \frac{172}{1375} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{3}{11})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 24x-\frac{18}{11}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x- \frac{126}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{-126} & = & \color{red}{-385x} +66 \\\Leftrightarrow & 1848x \color{red}{-126} \color{blue}{+126} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{+126} \\\Leftrightarrow & 1848x+385x& = & 66+126 \\\Leftrightarrow & \color{red}{2233} x& = & 192 \\\Leftrightarrow & x = \frac{192}{2233} & & \\ & V = \left\{ \frac{192}{2233} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{5}{7})& = & -5x+\frac{3}{8} \\\Leftrightarrow & 6x-\frac{10}{7}& = & -5x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{336}{ \color{blue}{56} }x- \frac{80}{ \color{blue}{56} })& = & (\frac{-280}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 336x \color{red}{-80} & = & \color{red}{-280x} +21 \\\Leftrightarrow & 336x \color{red}{-80} \color{blue}{+80} \color{blue}{+280x} & = & \color{red}{-280x} +21 \color{blue}{+280x} \color{blue}{+80} \\\Leftrightarrow & 336x+280x& = & 21+80 \\\Leftrightarrow & \color{red}{616} x& = & 101 \\\Leftrightarrow & x = \frac{101}{616} & & \\ & V = \left\{ \frac{101}{616} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{3}{4})& = & -6x+\frac{9}{2} \\\Leftrightarrow & 25x+\frac{15}{4}& = & -6x+\frac{9}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{100}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{-24}{ \color{blue}{4} }x+ \frac{18}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 100x \color{red}{+15} & = & \color{red}{-24x} +18 \\\Leftrightarrow & 100x \color{red}{+15} \color{blue}{-15} \color{blue}{+24x} & = & \color{red}{-24x} +18 \color{blue}{+24x} \color{blue}{-15} \\\Leftrightarrow & 100x+24x& = & 18-15 \\\Leftrightarrow & \color{red}{124} x& = & 3 \\\Leftrightarrow & x = \frac{3}{124} & & \\ & V = \left\{ \frac{3}{124} \right\} & \\\end{align}\)