Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{4}{7})& = & 5x+\frac{9}{7} \\\Leftrightarrow & 24x-\frac{24}{7}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{168}{ \color{blue}{7} }x- \frac{24}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 168x \color{red}{-24} & = & \color{red}{35x} +9 \\\Leftrightarrow & 168x \color{red}{-24} \color{blue}{+24} \color{blue}{-35x} & = & \color{red}{35x} +9 \color{blue}{-35x} \color{blue}{+24} \\\Leftrightarrow & 168x-35x& = & 9+24 \\\Leftrightarrow & \color{red}{133} x& = & 33 \\\Leftrightarrow & x = \frac{33}{133} & & \\ & V = \left\{ \frac{33}{133} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{3}{8})& = & 9x+\frac{10}{9} \\\Leftrightarrow & 28x-\frac{21}{8}& = & 9x+\frac{10}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{2016}{ \color{blue}{72} }x- \frac{189}{ \color{blue}{72} })& = & (\frac{648}{ \color{blue}{72} }x+ \frac{80}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 2016x \color{red}{-189} & = & \color{red}{648x} +80 \\\Leftrightarrow & 2016x \color{red}{-189} \color{blue}{+189} \color{blue}{-648x} & = & \color{red}{648x} +80 \color{blue}{-648x} \color{blue}{+189} \\\Leftrightarrow & 2016x-648x& = & 80+189 \\\Leftrightarrow & \color{red}{1368} x& = & 269 \\\Leftrightarrow & x = \frac{269}{1368} & & \\ & V = \left\{ \frac{269}{1368} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{4}{5})& = & 5x+\frac{7}{12} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-720}{ \color{blue}{60} }x+ \frac{144}{ \color{blue}{60} })& = & (\frac{300}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -720x \color{red}{+144} & = & \color{red}{300x} +35 \\\Leftrightarrow & -720x \color{red}{+144} \color{blue}{-144} \color{blue}{-300x} & = & \color{red}{300x} +35 \color{blue}{-300x} \color{blue}{-144} \\\Leftrightarrow & -720x-300x& = & 35-144 \\\Leftrightarrow & \color{red}{-1020} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{-1020} & & \\\Leftrightarrow & x = \frac{109}{1020} & & \\ & V = \left\{ \frac{109}{1020} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{5}{9})& = & 9x+\frac{6}{11} \\\Leftrightarrow & -35x-\frac{35}{9}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-3465}{ \color{blue}{99} }x- \frac{385}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -3465x \color{red}{-385} & = & \color{red}{891x} +54 \\\Leftrightarrow & -3465x \color{red}{-385} \color{blue}{+385} \color{blue}{-891x} & = & \color{red}{891x} +54 \color{blue}{-891x} \color{blue}{+385} \\\Leftrightarrow & -3465x-891x& = & 54+385 \\\Leftrightarrow & \color{red}{-4356} x& = & 439 \\\Leftrightarrow & x = \frac{439}{-4356} & & \\\Leftrightarrow & x = \frac{-439}{4356} & & \\ & V = \left\{ \frac{-439}{4356} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{4}{3})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 12x+\frac{16}{3}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{36}{ \color{blue}{3} }x+ \frac{16}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 36x \color{red}{+16} & = & \color{red}{15x} +4 \\\Leftrightarrow & 36x \color{red}{+16} \color{blue}{-16} \color{blue}{-15x} & = & \color{red}{15x} +4 \color{blue}{-15x} \color{blue}{-16} \\\Leftrightarrow & 36x-15x& = & 4-16 \\\Leftrightarrow & \color{red}{21} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{21} & & \\\Leftrightarrow & x = \frac{-4}{7} & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{2}{11})& = & 6x+\frac{10}{11} \\\Leftrightarrow & 25x+\frac{10}{11}& = & 6x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{275}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} })& = & (\frac{66}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 275x \color{red}{+10} & = & \color{red}{66x} +10 \\\Leftrightarrow & 275x \color{red}{+10} \color{blue}{-10} \color{blue}{-66x} & = & \color{red}{66x} +10 \color{blue}{-66x} \color{blue}{-10} \\\Leftrightarrow & 275x-66x& = & 10-10 \\\Leftrightarrow & \color{red}{209} x& = & 0 \\\Leftrightarrow & x = \frac{0}{209} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{2}{5})& = & 3x+\frac{4}{7} \\\Leftrightarrow & 14x+\frac{14}{5}& = & 3x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{490}{ \color{blue}{35} }x+ \frac{98}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 490x \color{red}{+98} & = & \color{red}{105x} +20 \\\Leftrightarrow & 490x \color{red}{+98} \color{blue}{-98} \color{blue}{-105x} & = & \color{red}{105x} +20 \color{blue}{-105x} \color{blue}{-98} \\\Leftrightarrow & 490x-105x& = & 20-98 \\\Leftrightarrow & \color{red}{385} x& = & -78 \\\Leftrightarrow & x = \frac{-78}{385} & & \\ & V = \left\{ \frac{-78}{385} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{3}{2})& = & 4x+\frac{9}{4} \\\Leftrightarrow & 15x-\frac{9}{2}& = & 4x+\frac{9}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{60}{ \color{blue}{4} }x- \frac{18}{ \color{blue}{4} })& = & (\frac{16}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 60x \color{red}{-18} & = & \color{red}{16x} +9 \\\Leftrightarrow & 60x \color{red}{-18} \color{blue}{+18} \color{blue}{-16x} & = & \color{red}{16x} +9 \color{blue}{-16x} \color{blue}{+18} \\\Leftrightarrow & 60x-16x& = & 9+18 \\\Leftrightarrow & \color{red}{44} x& = & 27 \\\Leftrightarrow & x = \frac{27}{44} & & \\ & V = \left\{ \frac{27}{44} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{5}{3})& = & -5x+\frac{7}{12} \\\Leftrightarrow & 12x-\frac{20}{3}& = & -5x+\frac{7}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{144}{ \color{blue}{12} }x- \frac{80}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 144x \color{red}{-80} & = & \color{red}{-60x} +7 \\\Leftrightarrow & 144x \color{red}{-80} \color{blue}{+80} \color{blue}{+60x} & = & \color{red}{-60x} +7 \color{blue}{+60x} \color{blue}{+80} \\\Leftrightarrow & 144x+60x& = & 7+80 \\\Leftrightarrow & \color{red}{204} x& = & 87 \\\Leftrightarrow & x = \frac{87}{204} & & \\\Leftrightarrow & x = \frac{29}{68} & & \\ & V = \left\{ \frac{29}{68} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{5}{7})& = & -9x+\frac{2}{11} \\\Leftrightarrow & 8x+\frac{20}{7}& = & -9x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{+220} & = & \color{red}{-693x} +14 \\\Leftrightarrow & 616x \color{red}{+220} \color{blue}{-220} \color{blue}{+693x} & = & \color{red}{-693x} +14 \color{blue}{+693x} \color{blue}{-220} \\\Leftrightarrow & 616x+693x& = & 14-220 \\\Leftrightarrow & \color{red}{1309} x& = & -206 \\\Leftrightarrow & x = \frac{-206}{1309} & & \\ & V = \left\{ \frac{-206}{1309} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{4}{7})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 8x-\frac{16}{7}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{56}{ \color{blue}{7} }x- \frac{16}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 56x \color{red}{-16} & = & \color{red}{-49x} +10 \\\Leftrightarrow & 56x \color{red}{-16} \color{blue}{+16} \color{blue}{+49x} & = & \color{red}{-49x} +10 \color{blue}{+49x} \color{blue}{+16} \\\Leftrightarrow & 56x+49x& = & 10+16 \\\Leftrightarrow & \color{red}{105} x& = & 26 \\\Leftrightarrow & x = \frac{26}{105} & & \\ & V = \left\{ \frac{26}{105} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{2}{5})& = & 5x+\frac{4}{11} \\\Leftrightarrow & 28x+\frac{14}{5}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1540}{ \color{blue}{55} }x+ \frac{154}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1540x \color{red}{+154} & = & \color{red}{275x} +20 \\\Leftrightarrow & 1540x \color{red}{+154} \color{blue}{-154} \color{blue}{-275x} & = & \color{red}{275x} +20 \color{blue}{-275x} \color{blue}{-154} \\\Leftrightarrow & 1540x-275x& = & 20-154 \\\Leftrightarrow & \color{red}{1265} x& = & -134 \\\Leftrightarrow & x = \frac{-134}{1265} & & \\ & V = \left\{ \frac{-134}{1265} \right\} & \\\end{align}\)