Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{5}{8})& = & 5x+\frac{6}{11} \\\Leftrightarrow & -12x-\frac{15}{8}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1056}{ \color{blue}{88} }x- \frac{165}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1056x \color{red}{-165} & = & \color{red}{440x} +48 \\\Leftrightarrow & -1056x \color{red}{-165} \color{blue}{+165} \color{blue}{-440x} & = & \color{red}{440x} +48 \color{blue}{-440x} \color{blue}{+165} \\\Leftrightarrow & -1056x-440x& = & 48+165 \\\Leftrightarrow & \color{red}{-1496} x& = & 213 \\\Leftrightarrow & x = \frac{213}{-1496} & & \\\Leftrightarrow & x = \frac{-213}{1496} & & \\ & V = \left\{ \frac{-213}{1496} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{5}{4})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -10x-\frac{25}{4}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-120}{ \color{blue}{12} }x- \frac{75}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -120x \color{red}{-75} & = & \color{red}{-84x} +16 \\\Leftrightarrow & -120x \color{red}{-75} \color{blue}{+75} \color{blue}{+84x} & = & \color{red}{-84x} +16 \color{blue}{+84x} \color{blue}{+75} \\\Leftrightarrow & -120x+84x& = & 16+75 \\\Leftrightarrow & \color{red}{-36} x& = & 91 \\\Leftrightarrow & x = \frac{91}{-36} & & \\\Leftrightarrow & x = \frac{-91}{36} & & \\ & V = \left\{ \frac{-91}{36} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{3}{2})& = & -2x+\frac{6}{11} \\\Leftrightarrow & 15x+\frac{9}{2}& = & -2x+\frac{6}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{330}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} })& = & (\frac{-44}{ \color{blue}{22} }x+ \frac{12}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 330x \color{red}{+99} & = & \color{red}{-44x} +12 \\\Leftrightarrow & 330x \color{red}{+99} \color{blue}{-99} \color{blue}{+44x} & = & \color{red}{-44x} +12 \color{blue}{+44x} \color{blue}{-99} \\\Leftrightarrow & 330x+44x& = & 12-99 \\\Leftrightarrow & \color{red}{374} x& = & -87 \\\Leftrightarrow & x = \frac{-87}{374} & & \\ & V = \left\{ \frac{-87}{374} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{4}{3})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 14x-\frac{28}{3}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x- \frac{308}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{-308} & = & \color{red}{-165x} +18 \\\Leftrightarrow & 462x \color{red}{-308} \color{blue}{+308} \color{blue}{+165x} & = & \color{red}{-165x} +18 \color{blue}{+165x} \color{blue}{+308} \\\Leftrightarrow & 462x+165x& = & 18+308 \\\Leftrightarrow & \color{red}{627} x& = & 326 \\\Leftrightarrow & x = \frac{326}{627} & & \\ & V = \left\{ \frac{326}{627} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{3}{11})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -30x+\frac{18}{11}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{+126} & = & \color{red}{539x} +110 \\\Leftrightarrow & -2310x \color{red}{+126} \color{blue}{-126} \color{blue}{-539x} & = & \color{red}{539x} +110 \color{blue}{-539x} \color{blue}{-126} \\\Leftrightarrow & -2310x-539x& = & 110-126 \\\Leftrightarrow & \color{red}{-2849} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-2849} & & \\\Leftrightarrow & x = \frac{16}{2849} & & \\ & V = \left\{ \frac{16}{2849} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{2}{3})& = & -3x+\frac{3}{5} \\\Leftrightarrow & -14x-\frac{14}{3}& = & -3x+\frac{3}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-210}{ \color{blue}{15} }x- \frac{70}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{9}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -210x \color{red}{-70} & = & \color{red}{-45x} +9 \\\Leftrightarrow & -210x \color{red}{-70} \color{blue}{+70} \color{blue}{+45x} & = & \color{red}{-45x} +9 \color{blue}{+45x} \color{blue}{+70} \\\Leftrightarrow & -210x+45x& = & 9+70 \\\Leftrightarrow & \color{red}{-165} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-165} & & \\\Leftrightarrow & x = \frac{-79}{165} & & \\ & V = \left\{ \frac{-79}{165} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{2}{5})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+36} & = & \color{red}{75x} +10 \\\Leftrightarrow & -180x \color{red}{+36} \color{blue}{-36} \color{blue}{-75x} & = & \color{red}{75x} +10 \color{blue}{-75x} \color{blue}{-36} \\\Leftrightarrow & -180x-75x& = & 10-36 \\\Leftrightarrow & \color{red}{-255} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-255} & & \\\Leftrightarrow & x = \frac{26}{255} & & \\ & V = \left\{ \frac{26}{255} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{5}{9})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 20x+\frac{20}{9}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x+ \frac{20}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{+20} & = & \color{red}{63x} +30 \\\Leftrightarrow & 180x \color{red}{+20} \color{blue}{-20} \color{blue}{-63x} & = & \color{red}{63x} +30 \color{blue}{-63x} \color{blue}{-20} \\\Leftrightarrow & 180x-63x& = & 30-20 \\\Leftrightarrow & \color{red}{117} x& = & 10 \\\Leftrightarrow & x = \frac{10}{117} & & \\ & V = \left\{ \frac{10}{117} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{4}{7})& = & -5x+\frac{5}{8} \\\Leftrightarrow & 12x-\frac{12}{7}& = & -5x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{672}{ \color{blue}{56} }x- \frac{96}{ \color{blue}{56} })& = & (\frac{-280}{ \color{blue}{56} }x+ \frac{35}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 672x \color{red}{-96} & = & \color{red}{-280x} +35 \\\Leftrightarrow & 672x \color{red}{-96} \color{blue}{+96} \color{blue}{+280x} & = & \color{red}{-280x} +35 \color{blue}{+280x} \color{blue}{+96} \\\Leftrightarrow & 672x+280x& = & 35+96 \\\Leftrightarrow & \color{red}{952} x& = & 131 \\\Leftrightarrow & x = \frac{131}{952} & & \\ & V = \left\{ \frac{131}{952} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{2}{9})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 6x-\frac{4}{9}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{108}{ \color{blue}{18} }x- \frac{8}{ \color{blue}{18} })& = & (\frac{-90}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 108x \color{red}{-8} & = & \color{red}{-90x} +27 \\\Leftrightarrow & 108x \color{red}{-8} \color{blue}{+8} \color{blue}{+90x} & = & \color{red}{-90x} +27 \color{blue}{+90x} \color{blue}{+8} \\\Leftrightarrow & 108x+90x& = & 27+8 \\\Leftrightarrow & \color{red}{198} x& = & 35 \\\Leftrightarrow & x = \frac{35}{198} & & \\ & V = \left\{ \frac{35}{198} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{5}{4})& = & 7x+\frac{9}{5} \\\Leftrightarrow & 15x+\frac{25}{4}& = & 7x+\frac{9}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{300}{ \color{blue}{20} }x+ \frac{125}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{36}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 300x \color{red}{+125} & = & \color{red}{140x} +36 \\\Leftrightarrow & 300x \color{red}{+125} \color{blue}{-125} \color{blue}{-140x} & = & \color{red}{140x} +36 \color{blue}{-140x} \color{blue}{-125} \\\Leftrightarrow & 300x-140x& = & 36-125 \\\Leftrightarrow & \color{red}{160} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{160} & & \\ & V = \left\{ \frac{-89}{160} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{4}{5})& = & 4x+\frac{7}{2} \\\Leftrightarrow & -15x+\frac{12}{5}& = & 4x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-150}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{40}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -150x \color{red}{+24} & = & \color{red}{40x} +35 \\\Leftrightarrow & -150x \color{red}{+24} \color{blue}{-24} \color{blue}{-40x} & = & \color{red}{40x} +35 \color{blue}{-40x} \color{blue}{-24} \\\Leftrightarrow & -150x-40x& = & 35-24 \\\Leftrightarrow & \color{red}{-190} x& = & 11 \\\Leftrightarrow & x = \frac{11}{-190} & & \\\Leftrightarrow & x = \frac{-11}{190} & & \\ & V = \left\{ \frac{-11}{190} \right\} & \\\end{align}\)