Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{3}{5})& = & 4x+\frac{7}{9} \\\Leftrightarrow & -15x-\frac{9}{5}& = & 4x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-675}{ \color{blue}{45} }x- \frac{81}{ \color{blue}{45} })& = & (\frac{180}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -675x \color{red}{-81} & = & \color{red}{180x} +35 \\\Leftrightarrow & -675x \color{red}{-81} \color{blue}{+81} \color{blue}{-180x} & = & \color{red}{180x} +35 \color{blue}{-180x} \color{blue}{+81} \\\Leftrightarrow & -675x-180x& = & 35+81 \\\Leftrightarrow & \color{red}{-855} x& = & 116 \\\Leftrightarrow & x = \frac{116}{-855} & & \\\Leftrightarrow & x = \frac{-116}{855} & & \\ & V = \left\{ \frac{-116}{855} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{4}{5})& = & 5x+\frac{7}{4} \\\Leftrightarrow & 12x+\frac{24}{5}& = & 5x+\frac{7}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{240}{ \color{blue}{20} }x+ \frac{96}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{35}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 240x \color{red}{+96} & = & \color{red}{100x} +35 \\\Leftrightarrow & 240x \color{red}{+96} \color{blue}{-96} \color{blue}{-100x} & = & \color{red}{100x} +35 \color{blue}{-100x} \color{blue}{-96} \\\Leftrightarrow & 240x-100x& = & 35-96 \\\Leftrightarrow & \color{red}{140} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{140} & & \\ & V = \left\{ \frac{-61}{140} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{2}{5})& = & 8x+\frac{3}{2} \\\Leftrightarrow & 9x-\frac{6}{5}& = & 8x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{90}{ \color{blue}{10} }x- \frac{12}{ \color{blue}{10} })& = & (\frac{80}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 90x \color{red}{-12} & = & \color{red}{80x} +15 \\\Leftrightarrow & 90x \color{red}{-12} \color{blue}{+12} \color{blue}{-80x} & = & \color{red}{80x} +15 \color{blue}{-80x} \color{blue}{+12} \\\Leftrightarrow & 90x-80x& = & 15+12 \\\Leftrightarrow & \color{red}{10} x& = & 27 \\\Leftrightarrow & x = \frac{27}{10} & & \\ & V = \left\{ \frac{27}{10} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{5}{2})& = & 5x+\frac{4}{9} \\\Leftrightarrow & 28x+\frac{35}{2}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{504}{ \color{blue}{18} }x+ \frac{315}{ \color{blue}{18} })& = & (\frac{90}{ \color{blue}{18} }x+ \frac{8}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 504x \color{red}{+315} & = & \color{red}{90x} +8 \\\Leftrightarrow & 504x \color{red}{+315} \color{blue}{-315} \color{blue}{-90x} & = & \color{red}{90x} +8 \color{blue}{-90x} \color{blue}{-315} \\\Leftrightarrow & 504x-90x& = & 8-315 \\\Leftrightarrow & \color{red}{414} x& = & -307 \\\Leftrightarrow & x = \frac{-307}{414} & & \\ & V = \left\{ \frac{-307}{414} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{5}{3})& = & -9x+\frac{4}{3} \\\Leftrightarrow & -8x-\frac{20}{3}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-24}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{-27}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -24x \color{red}{-20} & = & \color{red}{-27x} +4 \\\Leftrightarrow & -24x \color{red}{-20} \color{blue}{+20} \color{blue}{+27x} & = & \color{red}{-27x} +4 \color{blue}{+27x} \color{blue}{+20} \\\Leftrightarrow & -24x+27x& = & 4+20 \\\Leftrightarrow & \color{red}{3} x& = & 24 \\\Leftrightarrow & x = \frac{24}{3} & & \\\Leftrightarrow & x = 8 & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{5}{8})& = & 2x+\frac{3}{4} \\\Leftrightarrow & 9x+\frac{15}{8}& = & 2x+\frac{3}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{72}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{16}{ \color{blue}{8} }x+ \frac{6}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 72x \color{red}{+15} & = & \color{red}{16x} +6 \\\Leftrightarrow & 72x \color{red}{+15} \color{blue}{-15} \color{blue}{-16x} & = & \color{red}{16x} +6 \color{blue}{-16x} \color{blue}{-15} \\\Leftrightarrow & 72x-16x& = & 6-15 \\\Leftrightarrow & \color{red}{56} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{56} & & \\ & V = \left\{ \frac{-9}{56} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{5}{2})& = & 8x+\frac{5}{6} \\\Leftrightarrow & -15x+\frac{25}{2}& = & 8x+\frac{5}{6} \\ & & & \text{kgv van noemers 2 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-90}{ \color{blue}{6} }x+ \frac{75}{ \color{blue}{6} })& = & (\frac{48}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -90x \color{red}{+75} & = & \color{red}{48x} +5 \\\Leftrightarrow & -90x \color{red}{+75} \color{blue}{-75} \color{blue}{-48x} & = & \color{red}{48x} +5 \color{blue}{-48x} \color{blue}{-75} \\\Leftrightarrow & -90x-48x& = & 5-75 \\\Leftrightarrow & \color{red}{-138} x& = & -70 \\\Leftrightarrow & x = \frac{-70}{-138} & & \\\Leftrightarrow & x = \frac{35}{69} & & \\ & V = \left\{ \frac{35}{69} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{2}{5})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 4x-\frac{4}{5}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{220}{ \color{blue}{55} }x- \frac{44}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 220x \color{red}{-44} & = & \color{red}{-385x} +30 \\\Leftrightarrow & 220x \color{red}{-44} \color{blue}{+44} \color{blue}{+385x} & = & \color{red}{-385x} +30 \color{blue}{+385x} \color{blue}{+44} \\\Leftrightarrow & 220x+385x& = & 30+44 \\\Leftrightarrow & \color{red}{605} x& = & 74 \\\Leftrightarrow & x = \frac{74}{605} & & \\ & V = \left\{ \frac{74}{605} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{3}{5})& = & 8x+\frac{10}{11} \\\Leftrightarrow & -15x-\frac{9}{5}& = & 8x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x- \frac{99}{ \color{blue}{55} })& = & (\frac{440}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{-99} & = & \color{red}{440x} +50 \\\Leftrightarrow & -825x \color{red}{-99} \color{blue}{+99} \color{blue}{-440x} & = & \color{red}{440x} +50 \color{blue}{-440x} \color{blue}{+99} \\\Leftrightarrow & -825x-440x& = & 50+99 \\\Leftrightarrow & \color{red}{-1265} x& = & 149 \\\Leftrightarrow & x = \frac{149}{-1265} & & \\\Leftrightarrow & x = \frac{-149}{1265} & & \\ & V = \left\{ \frac{-149}{1265} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{5}{11})& = & -5x+\frac{8}{3} \\\Leftrightarrow & -12x-\frac{30}{11}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x- \frac{90}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{-90} & = & \color{red}{-165x} +88 \\\Leftrightarrow & -396x \color{red}{-90} \color{blue}{+90} \color{blue}{+165x} & = & \color{red}{-165x} +88 \color{blue}{+165x} \color{blue}{+90} \\\Leftrightarrow & -396x+165x& = & 88+90 \\\Leftrightarrow & \color{red}{-231} x& = & 178 \\\Leftrightarrow & x = \frac{178}{-231} & & \\\Leftrightarrow & x = \frac{-178}{231} & & \\ & V = \left\{ \frac{-178}{231} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{5}{3})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -10x+\frac{25}{3}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x+ \frac{275}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{+275} & = & \color{red}{-231x} +18 \\\Leftrightarrow & -330x \color{red}{+275} \color{blue}{-275} \color{blue}{+231x} & = & \color{red}{-231x} +18 \color{blue}{+231x} \color{blue}{-275} \\\Leftrightarrow & -330x+231x& = & 18-275 \\\Leftrightarrow & \color{red}{-99} x& = & -257 \\\Leftrightarrow & x = \frac{-257}{-99} & & \\\Leftrightarrow & x = \frac{257}{99} & & \\ & V = \left\{ \frac{257}{99} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{2}{11})& = & -4x+\frac{7}{12} \\\Leftrightarrow & -15x+\frac{6}{11}& = & -4x+\frac{7}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-1980}{ \color{blue}{132} }x+ \frac{72}{ \color{blue}{132} })& = & (\frac{-528}{ \color{blue}{132} }x+ \frac{77}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -1980x \color{red}{+72} & = & \color{red}{-528x} +77 \\\Leftrightarrow & -1980x \color{red}{+72} \color{blue}{-72} \color{blue}{+528x} & = & \color{red}{-528x} +77 \color{blue}{+528x} \color{blue}{-72} \\\Leftrightarrow & -1980x+528x& = & 77-72 \\\Leftrightarrow & \color{red}{-1452} x& = & 5 \\\Leftrightarrow & x = \frac{5}{-1452} & & \\\Leftrightarrow & x = \frac{-5}{1452} & & \\ & V = \left\{ \frac{-5}{1452} \right\} & \\\end{align}\)