Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{5}{11})& = & 5x+\frac{8}{9} \\\Leftrightarrow & 6x+\frac{10}{11}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{594}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 594x \color{red}{+90} & = & \color{red}{495x} +88 \\\Leftrightarrow & 594x \color{red}{+90} \color{blue}{-90} \color{blue}{-495x} & = & \color{red}{495x} +88 \color{blue}{-495x} \color{blue}{-90} \\\Leftrightarrow & 594x-495x& = & 88-90 \\\Leftrightarrow & \color{red}{99} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{99} & & \\ & V = \left\{ \frac{-2}{99} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{3}{8})& = & -4x+\frac{6}{11} \\\Leftrightarrow & 21x+\frac{21}{8}& = & -4x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1848}{ \color{blue}{88} }x+ \frac{231}{ \color{blue}{88} })& = & (\frac{-352}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1848x \color{red}{+231} & = & \color{red}{-352x} +48 \\\Leftrightarrow & 1848x \color{red}{+231} \color{blue}{-231} \color{blue}{+352x} & = & \color{red}{-352x} +48 \color{blue}{+352x} \color{blue}{-231} \\\Leftrightarrow & 1848x+352x& = & 48-231 \\\Leftrightarrow & \color{red}{2200} x& = & -183 \\\Leftrightarrow & x = \frac{-183}{2200} & & \\ & V = \left\{ \frac{-183}{2200} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{8})& = & 9x+\frac{9}{10} \\\Leftrightarrow & 14x-\frac{35}{8}& = & 9x+\frac{9}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{560}{ \color{blue}{40} }x- \frac{175}{ \color{blue}{40} })& = & (\frac{360}{ \color{blue}{40} }x+ \frac{36}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 560x \color{red}{-175} & = & \color{red}{360x} +36 \\\Leftrightarrow & 560x \color{red}{-175} \color{blue}{+175} \color{blue}{-360x} & = & \color{red}{360x} +36 \color{blue}{-360x} \color{blue}{+175} \\\Leftrightarrow & 560x-360x& = & 36+175 \\\Leftrightarrow & \color{red}{200} x& = & 211 \\\Leftrightarrow & x = \frac{211}{200} & & \\ & V = \left\{ \frac{211}{200} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{5}{6})& = & -4x+\frac{7}{4} \\\Leftrightarrow & -15x+\frac{25}{6}& = & -4x+\frac{7}{4} \\ & & & \text{kgv van noemers 6 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-180}{ \color{blue}{12} }x+ \frac{50}{ \color{blue}{12} })& = & (\frac{-48}{ \color{blue}{12} }x+ \frac{21}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -180x \color{red}{+50} & = & \color{red}{-48x} +21 \\\Leftrightarrow & -180x \color{red}{+50} \color{blue}{-50} \color{blue}{+48x} & = & \color{red}{-48x} +21 \color{blue}{+48x} \color{blue}{-50} \\\Leftrightarrow & -180x+48x& = & 21-50 \\\Leftrightarrow & \color{red}{-132} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-132} & & \\\Leftrightarrow & x = \frac{29}{132} & & \\ & V = \left\{ \frac{29}{132} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{6})& = & -5x+\frac{2}{7} \\\Leftrightarrow & 14x-\frac{35}{6}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{588}{ \color{blue}{42} }x- \frac{245}{ \color{blue}{42} })& = & (\frac{-210}{ \color{blue}{42} }x+ \frac{12}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 588x \color{red}{-245} & = & \color{red}{-210x} +12 \\\Leftrightarrow & 588x \color{red}{-245} \color{blue}{+245} \color{blue}{+210x} & = & \color{red}{-210x} +12 \color{blue}{+210x} \color{blue}{+245} \\\Leftrightarrow & 588x+210x& = & 12+245 \\\Leftrightarrow & \color{red}{798} x& = & 257 \\\Leftrightarrow & x = \frac{257}{798} & & \\ & V = \left\{ \frac{257}{798} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{4}{5})& = & -5x+\frac{5}{8} \\\Leftrightarrow & -12x-\frac{24}{5}& = & -5x+\frac{5}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-480}{ \color{blue}{40} }x- \frac{192}{ \color{blue}{40} })& = & (\frac{-200}{ \color{blue}{40} }x+ \frac{25}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -480x \color{red}{-192} & = & \color{red}{-200x} +25 \\\Leftrightarrow & -480x \color{red}{-192} \color{blue}{+192} \color{blue}{+200x} & = & \color{red}{-200x} +25 \color{blue}{+200x} \color{blue}{+192} \\\Leftrightarrow & -480x+200x& = & 25+192 \\\Leftrightarrow & \color{red}{-280} x& = & 217 \\\Leftrightarrow & x = \frac{217}{-280} & & \\\Leftrightarrow & x = \frac{-31}{40} & & \\ & V = \left\{ \frac{-31}{40} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-1)& = & 8x+\frac{3}{10} \\\Leftrightarrow & -21x+7& = & 8x+\frac{3}{10} \\ & & & \text{kgv van noemers 1 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-210}{ \color{blue}{10} }x+ \frac{70}{ \color{blue}{10} })& = & (\frac{80}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -210x \color{red}{+70} & = & \color{red}{80x} +3 \\\Leftrightarrow & -210x \color{red}{+70} \color{blue}{-70} \color{blue}{-80x} & = & \color{red}{80x} +3 \color{blue}{-80x} \color{blue}{-70} \\\Leftrightarrow & -210x-80x& = & 3-70 \\\Leftrightarrow & \color{red}{-290} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{-290} & & \\\Leftrightarrow & x = \frac{67}{290} & & \\ & V = \left\{ \frac{67}{290} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{3}{11})& = & 5x+\frac{10}{11} \\\Leftrightarrow & -4x+\frac{6}{11}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-44}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -44x \color{red}{+6} & = & \color{red}{55x} +10 \\\Leftrightarrow & -44x \color{red}{+6} \color{blue}{-6} \color{blue}{-55x} & = & \color{red}{55x} +10 \color{blue}{-55x} \color{blue}{-6} \\\Leftrightarrow & -44x-55x& = & 10-6 \\\Leftrightarrow & \color{red}{-99} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-99} & & \\\Leftrightarrow & x = \frac{-4}{99} & & \\ & V = \left\{ \frac{-4}{99} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{3}{7})& = & -2x+\frac{5}{6} \\\Leftrightarrow & 25x-\frac{15}{7}& = & -2x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{1050}{ \color{blue}{42} }x- \frac{90}{ \color{blue}{42} })& = & (\frac{-84}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 1050x \color{red}{-90} & = & \color{red}{-84x} +35 \\\Leftrightarrow & 1050x \color{red}{-90} \color{blue}{+90} \color{blue}{+84x} & = & \color{red}{-84x} +35 \color{blue}{+84x} \color{blue}{+90} \\\Leftrightarrow & 1050x+84x& = & 35+90 \\\Leftrightarrow & \color{red}{1134} x& = & 125 \\\Leftrightarrow & x = \frac{125}{1134} & & \\ & V = \left\{ \frac{125}{1134} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{2}{9})& = & 9x+\frac{8}{5} \\\Leftrightarrow & -20x+\frac{8}{9}& = & 9x+\frac{8}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-900}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{72}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -900x \color{red}{+40} & = & \color{red}{405x} +72 \\\Leftrightarrow & -900x \color{red}{+40} \color{blue}{-40} \color{blue}{-405x} & = & \color{red}{405x} +72 \color{blue}{-405x} \color{blue}{-40} \\\Leftrightarrow & -900x-405x& = & 72-40 \\\Leftrightarrow & \color{red}{-1305} x& = & 32 \\\Leftrightarrow & x = \frac{32}{-1305} & & \\\Leftrightarrow & x = \frac{-32}{1305} & & \\ & V = \left\{ \frac{-32}{1305} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{3}{2})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 10x+\frac{15}{2}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{20}{ \color{blue}{2} }x+ \frac{15}{ \color{blue}{2} })& = & (\frac{-14}{ \color{blue}{2} }x+ \frac{3}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 20x \color{red}{+15} & = & \color{red}{-14x} +3 \\\Leftrightarrow & 20x \color{red}{+15} \color{blue}{-15} \color{blue}{+14x} & = & \color{red}{-14x} +3 \color{blue}{+14x} \color{blue}{-15} \\\Leftrightarrow & 20x+14x& = & 3-15 \\\Leftrightarrow & \color{red}{34} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{34} & & \\\Leftrightarrow & x = \frac{-6}{17} & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{3}{5})& = & -5x+\frac{3}{11} \\\Leftrightarrow & 6x-\frac{9}{5}& = & -5x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x- \frac{99}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{-99} & = & \color{red}{-275x} +15 \\\Leftrightarrow & 330x \color{red}{-99} \color{blue}{+99} \color{blue}{+275x} & = & \color{red}{-275x} +15 \color{blue}{+275x} \color{blue}{+99} \\\Leftrightarrow & 330x+275x& = & 15+99 \\\Leftrightarrow & \color{red}{605} x& = & 114 \\\Leftrightarrow & x = \frac{114}{605} & & \\ & V = \left\{ \frac{114}{605} \right\} & \\\end{align}\)