Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{2}{9})& = & 9x+\frac{3}{10} \\\Leftrightarrow & -20x-\frac{8}{9}& = & 9x+\frac{3}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-1800}{ \color{blue}{90} }x- \frac{80}{ \color{blue}{90} })& = & (\frac{810}{ \color{blue}{90} }x+ \frac{27}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -1800x \color{red}{-80} & = & \color{red}{810x} +27 \\\Leftrightarrow & -1800x \color{red}{-80} \color{blue}{+80} \color{blue}{-810x} & = & \color{red}{810x} +27 \color{blue}{-810x} \color{blue}{+80} \\\Leftrightarrow & -1800x-810x& = & 27+80 \\\Leftrightarrow & \color{red}{-2610} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-2610} & & \\\Leftrightarrow & x = \frac{-107}{2610} & & \\ & V = \left\{ \frac{-107}{2610} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{3}{11})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -12x+\frac{12}{11}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x+ \frac{36}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{+36} & = & \color{red}{165x} +88 \\\Leftrightarrow & -396x \color{red}{+36} \color{blue}{-36} \color{blue}{-165x} & = & \color{red}{165x} +88 \color{blue}{-165x} \color{blue}{-36} \\\Leftrightarrow & -396x-165x& = & 88-36 \\\Leftrightarrow & \color{red}{-561} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-561} & & \\\Leftrightarrow & x = \frac{-52}{561} & & \\ & V = \left\{ \frac{-52}{561} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{2}{7})& = & -5x+\frac{2}{5} \\\Leftrightarrow & 6x-\frac{4}{7}& = & -5x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{20}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-20} & = & \color{red}{-175x} +14 \\\Leftrightarrow & 210x \color{red}{-20} \color{blue}{+20} \color{blue}{+175x} & = & \color{red}{-175x} +14 \color{blue}{+175x} \color{blue}{+20} \\\Leftrightarrow & 210x+175x& = & 14+20 \\\Leftrightarrow & \color{red}{385} x& = & 34 \\\Leftrightarrow & x = \frac{34}{385} & & \\ & V = \left\{ \frac{34}{385} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{2}{3})& = & 3x+\frac{9}{7} \\\Leftrightarrow & 8x+\frac{8}{3}& = & 3x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{+56} & = & \color{red}{63x} +27 \\\Leftrightarrow & 168x \color{red}{+56} \color{blue}{-56} \color{blue}{-63x} & = & \color{red}{63x} +27 \color{blue}{-63x} \color{blue}{-56} \\\Leftrightarrow & 168x-63x& = & 27-56 \\\Leftrightarrow & \color{red}{105} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{105} & & \\ & V = \left\{ \frac{-29}{105} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{3}{7})& = & 3x+\frac{9}{7} \\\Leftrightarrow & -8x-\frac{6}{7}& = & 3x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-56}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{21}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -56x \color{red}{-6} & = & \color{red}{21x} +9 \\\Leftrightarrow & -56x \color{red}{-6} \color{blue}{+6} \color{blue}{-21x} & = & \color{red}{21x} +9 \color{blue}{-21x} \color{blue}{+6} \\\Leftrightarrow & -56x-21x& = & 9+6 \\\Leftrightarrow & \color{red}{-77} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-77} & & \\\Leftrightarrow & x = \frac{-15}{77} & & \\ & V = \left\{ \frac{-15}{77} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{3}{7})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 6x-\frac{6}{7}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-30} & = & \color{red}{-175x} +42 \\\Leftrightarrow & 210x \color{red}{-30} \color{blue}{+30} \color{blue}{+175x} & = & \color{red}{-175x} +42 \color{blue}{+175x} \color{blue}{+30} \\\Leftrightarrow & 210x+175x& = & 42+30 \\\Leftrightarrow & \color{red}{385} x& = & 72 \\\Leftrightarrow & x = \frac{72}{385} & & \\ & V = \left\{ \frac{72}{385} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{3}{4})& = & -6x+\frac{5}{3} \\\Leftrightarrow & -25x+\frac{15}{4}& = & -6x+\frac{5}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-300}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{-72}{ \color{blue}{12} }x+ \frac{20}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -300x \color{red}{+45} & = & \color{red}{-72x} +20 \\\Leftrightarrow & -300x \color{red}{+45} \color{blue}{-45} \color{blue}{+72x} & = & \color{red}{-72x} +20 \color{blue}{+72x} \color{blue}{-45} \\\Leftrightarrow & -300x+72x& = & 20-45 \\\Leftrightarrow & \color{red}{-228} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{-228} & & \\\Leftrightarrow & x = \frac{25}{228} & & \\ & V = \left\{ \frac{25}{228} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{2}{3})& = & 8x+\frac{9}{10} \\\Leftrightarrow & -21x+\frac{14}{3}& = & 8x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-630}{ \color{blue}{30} }x+ \frac{140}{ \color{blue}{30} })& = & (\frac{240}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -630x \color{red}{+140} & = & \color{red}{240x} +27 \\\Leftrightarrow & -630x \color{red}{+140} \color{blue}{-140} \color{blue}{-240x} & = & \color{red}{240x} +27 \color{blue}{-240x} \color{blue}{-140} \\\Leftrightarrow & -630x-240x& = & 27-140 \\\Leftrightarrow & \color{red}{-870} x& = & -113 \\\Leftrightarrow & x = \frac{-113}{-870} & & \\\Leftrightarrow & x = \frac{113}{870} & & \\ & V = \left\{ \frac{113}{870} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{2}{11})& = & 5x+\frac{7}{5} \\\Leftrightarrow & -9x-\frac{6}{11}& = & 5x+\frac{7}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-495}{ \color{blue}{55} }x- \frac{30}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{77}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -495x \color{red}{-30} & = & \color{red}{275x} +77 \\\Leftrightarrow & -495x \color{red}{-30} \color{blue}{+30} \color{blue}{-275x} & = & \color{red}{275x} +77 \color{blue}{-275x} \color{blue}{+30} \\\Leftrightarrow & -495x-275x& = & 77+30 \\\Leftrightarrow & \color{red}{-770} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-770} & & \\\Leftrightarrow & x = \frac{-107}{770} & & \\ & V = \left\{ \frac{-107}{770} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{1}{2})& = & -9x+\frac{3}{2} \\\Leftrightarrow & 14x+\frac{7}{2}& = & -9x+\frac{3}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{28}{ \color{blue}{2} }x+ \frac{7}{ \color{blue}{2} })& = & (\frac{-18}{ \color{blue}{2} }x+ \frac{3}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 28x \color{red}{+7} & = & \color{red}{-18x} +3 \\\Leftrightarrow & 28x \color{red}{+7} \color{blue}{-7} \color{blue}{+18x} & = & \color{red}{-18x} +3 \color{blue}{+18x} \color{blue}{-7} \\\Leftrightarrow & 28x+18x& = & 3-7 \\\Leftrightarrow & \color{red}{46} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{46} & & \\\Leftrightarrow & x = \frac{-2}{23} & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{5}{12})& = & -9x+\frac{2}{11} \\\Leftrightarrow & 20x+\frac{25}{12}& = & -9x+\frac{2}{11} \\ & & & \text{kgv van noemers 12 en 11 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{2640}{ \color{blue}{132} }x+ \frac{275}{ \color{blue}{132} })& = & (\frac{-1188}{ \color{blue}{132} }x+ \frac{24}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 2640x \color{red}{+275} & = & \color{red}{-1188x} +24 \\\Leftrightarrow & 2640x \color{red}{+275} \color{blue}{-275} \color{blue}{+1188x} & = & \color{red}{-1188x} +24 \color{blue}{+1188x} \color{blue}{-275} \\\Leftrightarrow & 2640x+1188x& = & 24-275 \\\Leftrightarrow & \color{red}{3828} x& = & -251 \\\Leftrightarrow & x = \frac{-251}{3828} & & \\ & V = \left\{ \frac{-251}{3828} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{2}{3})& = & -3x+\frac{9}{2} \\\Leftrightarrow & 16x+\frac{8}{3}& = & -3x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{96}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{-18}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 96x \color{red}{+16} & = & \color{red}{-18x} +27 \\\Leftrightarrow & 96x \color{red}{+16} \color{blue}{-16} \color{blue}{+18x} & = & \color{red}{-18x} +27 \color{blue}{+18x} \color{blue}{-16} \\\Leftrightarrow & 96x+18x& = & 27-16 \\\Leftrightarrow & \color{red}{114} x& = & 11 \\\Leftrightarrow & x = \frac{11}{114} & & \\ & V = \left\{ \frac{11}{114} \right\} & \\\end{align}\)