Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{3}{11})& = & 5x+\frac{9}{4} \\\Leftrightarrow & 12x+\frac{18}{11}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{528}{ \color{blue}{44} }x+ \frac{72}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 528x \color{red}{+72} & = & \color{red}{220x} +99 \\\Leftrightarrow & 528x \color{red}{+72} \color{blue}{-72} \color{blue}{-220x} & = & \color{red}{220x} +99 \color{blue}{-220x} \color{blue}{-72} \\\Leftrightarrow & 528x-220x& = & 99-72 \\\Leftrightarrow & \color{red}{308} x& = & 27 \\\Leftrightarrow & x = \frac{27}{308} & & \\ & V = \left\{ \frac{27}{308} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{4}{5})& = & -5x+\frac{2}{11} \\\Leftrightarrow & 6x-\frac{12}{5}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{-132} & = & \color{red}{-275x} +10 \\\Leftrightarrow & 330x \color{red}{-132} \color{blue}{+132} \color{blue}{+275x} & = & \color{red}{-275x} +10 \color{blue}{+275x} \color{blue}{+132} \\\Leftrightarrow & 330x+275x& = & 10+132 \\\Leftrightarrow & \color{red}{605} x& = & 142 \\\Leftrightarrow & x = \frac{142}{605} & & \\ & V = \left\{ \frac{142}{605} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{2}{5})& = & 5x+\frac{7}{5} \\\Leftrightarrow & 24x-\frac{12}{5}& = & 5x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{120}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 120x \color{red}{-12} & = & \color{red}{25x} +7 \\\Leftrightarrow & 120x \color{red}{-12} \color{blue}{+12} \color{blue}{-25x} & = & \color{red}{25x} +7 \color{blue}{-25x} \color{blue}{+12} \\\Leftrightarrow & 120x-25x& = & 7+12 \\\Leftrightarrow & \color{red}{95} x& = & 19 \\\Leftrightarrow & x = \frac{19}{95} & & \\\Leftrightarrow & x = \frac{1}{5} & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{5}{4})& = & -4x+\frac{9}{2} \\\Leftrightarrow & -35x-\frac{35}{4}& = & -4x+\frac{9}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-140}{ \color{blue}{4} }x- \frac{35}{ \color{blue}{4} })& = & (\frac{-16}{ \color{blue}{4} }x+ \frac{18}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -140x \color{red}{-35} & = & \color{red}{-16x} +18 \\\Leftrightarrow & -140x \color{red}{-35} \color{blue}{+35} \color{blue}{+16x} & = & \color{red}{-16x} +18 \color{blue}{+16x} \color{blue}{+35} \\\Leftrightarrow & -140x+16x& = & 18+35 \\\Leftrightarrow & \color{red}{-124} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-124} & & \\\Leftrightarrow & x = \frac{-53}{124} & & \\ & V = \left\{ \frac{-53}{124} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{3}{5})& = & -3x+\frac{5}{7} \\\Leftrightarrow & -20x-\frac{12}{5}& = & -3x+\frac{5}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{25}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{-84} & = & \color{red}{-105x} +25 \\\Leftrightarrow & -700x \color{red}{-84} \color{blue}{+84} \color{blue}{+105x} & = & \color{red}{-105x} +25 \color{blue}{+105x} \color{blue}{+84} \\\Leftrightarrow & -700x+105x& = & 25+84 \\\Leftrightarrow & \color{red}{-595} x& = & 109 \\\Leftrightarrow & x = \frac{109}{-595} & & \\\Leftrightarrow & x = \frac{-109}{595} & & \\ & V = \left\{ \frac{-109}{595} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{4}{5})& = & -2x+\frac{5}{12} \\\Leftrightarrow & 9x-\frac{12}{5}& = & -2x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{540}{ \color{blue}{60} }x- \frac{144}{ \color{blue}{60} })& = & (\frac{-120}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 540x \color{red}{-144} & = & \color{red}{-120x} +25 \\\Leftrightarrow & 540x \color{red}{-144} \color{blue}{+144} \color{blue}{+120x} & = & \color{red}{-120x} +25 \color{blue}{+120x} \color{blue}{+144} \\\Leftrightarrow & 540x+120x& = & 25+144 \\\Leftrightarrow & \color{red}{660} x& = & 169 \\\Leftrightarrow & x = \frac{169}{660} & & \\ & V = \left\{ \frac{169}{660} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{2}{3})& = & 7x+\frac{6}{7} \\\Leftrightarrow & 16x-\frac{8}{3}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{-56} & = & \color{red}{147x} +18 \\\Leftrightarrow & 336x \color{red}{-56} \color{blue}{+56} \color{blue}{-147x} & = & \color{red}{147x} +18 \color{blue}{-147x} \color{blue}{+56} \\\Leftrightarrow & 336x-147x& = & 18+56 \\\Leftrightarrow & \color{red}{189} x& = & 74 \\\Leftrightarrow & x = \frac{74}{189} & & \\ & V = \left\{ \frac{74}{189} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{2}{3})& = & -8x+\frac{7}{2} \\\Leftrightarrow & -15x+\frac{10}{3}& = & -8x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-90}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} })& = & (\frac{-48}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -90x \color{red}{+20} & = & \color{red}{-48x} +21 \\\Leftrightarrow & -90x \color{red}{+20} \color{blue}{-20} \color{blue}{+48x} & = & \color{red}{-48x} +21 \color{blue}{+48x} \color{blue}{-20} \\\Leftrightarrow & -90x+48x& = & 21-20 \\\Leftrightarrow & \color{red}{-42} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-42} & & \\\Leftrightarrow & x = \frac{-1}{42} & & \\ & V = \left\{ \frac{-1}{42} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{3}{11})& = & 5x+\frac{9}{10} \\\Leftrightarrow & 18x-\frac{18}{11}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1980}{ \color{blue}{110} }x- \frac{180}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1980x \color{red}{-180} & = & \color{red}{550x} +99 \\\Leftrightarrow & 1980x \color{red}{-180} \color{blue}{+180} \color{blue}{-550x} & = & \color{red}{550x} +99 \color{blue}{-550x} \color{blue}{+180} \\\Leftrightarrow & 1980x-550x& = & 99+180 \\\Leftrightarrow & \color{red}{1430} x& = & 279 \\\Leftrightarrow & x = \frac{279}{1430} & & \\ & V = \left\{ \frac{279}{1430} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{4}{3})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -10x+\frac{20}{3}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-150}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -150x \color{red}{+100} & = & \color{red}{105x} +18 \\\Leftrightarrow & -150x \color{red}{+100} \color{blue}{-100} \color{blue}{-105x} & = & \color{red}{105x} +18 \color{blue}{-105x} \color{blue}{-100} \\\Leftrightarrow & -150x-105x& = & 18-100 \\\Leftrightarrow & \color{red}{-255} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{-255} & & \\\Leftrightarrow & x = \frac{82}{255} & & \\ & V = \left\{ \frac{82}{255} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{3}{7})& = & -3x+\frac{7}{4} \\\Leftrightarrow & -20x-\frac{12}{7}& = & -3x+\frac{7}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-560}{ \color{blue}{28} }x- \frac{48}{ \color{blue}{28} })& = & (\frac{-84}{ \color{blue}{28} }x+ \frac{49}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -560x \color{red}{-48} & = & \color{red}{-84x} +49 \\\Leftrightarrow & -560x \color{red}{-48} \color{blue}{+48} \color{blue}{+84x} & = & \color{red}{-84x} +49 \color{blue}{+84x} \color{blue}{+48} \\\Leftrightarrow & -560x+84x& = & 49+48 \\\Leftrightarrow & \color{red}{-476} x& = & 97 \\\Leftrightarrow & x = \frac{97}{-476} & & \\\Leftrightarrow & x = \frac{-97}{476} & & \\ & V = \left\{ \frac{-97}{476} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{3})& = & -5x+\frac{10}{7} \\\Leftrightarrow & -12x-\frac{20}{3}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{-140} & = & \color{red}{-105x} +30 \\\Leftrightarrow & -252x \color{red}{-140} \color{blue}{+140} \color{blue}{+105x} & = & \color{red}{-105x} +30 \color{blue}{+105x} \color{blue}{+140} \\\Leftrightarrow & -252x+105x& = & 30+140 \\\Leftrightarrow & \color{red}{-147} x& = & 170 \\\Leftrightarrow & x = \frac{170}{-147} & & \\\Leftrightarrow & x = \frac{-170}{147} & & \\ & V = \left\{ \frac{-170}{147} \right\} & \\\end{align}\)