Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{5}{6})& = & 8x+\frac{8}{3} \\\Leftrightarrow & 21x+\frac{35}{6}& = & 8x+\frac{8}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{126}{ \color{blue}{6} }x+ \frac{35}{ \color{blue}{6} })& = & (\frac{48}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 126x \color{red}{+35} & = & \color{red}{48x} +16 \\\Leftrightarrow & 126x \color{red}{+35} \color{blue}{-35} \color{blue}{-48x} & = & \color{red}{48x} +16 \color{blue}{-48x} \color{blue}{-35} \\\Leftrightarrow & 126x-48x& = & 16-35 \\\Leftrightarrow & \color{red}{78} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{78} & & \\ & V = \left\{ \frac{-19}{78} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{5}{7})& = & -9x+\frac{10}{3} \\\Leftrightarrow & -18x+\frac{30}{7}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-378}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -378x \color{red}{+90} & = & \color{red}{-189x} +70 \\\Leftrightarrow & -378x \color{red}{+90} \color{blue}{-90} \color{blue}{+189x} & = & \color{red}{-189x} +70 \color{blue}{+189x} \color{blue}{-90} \\\Leftrightarrow & -378x+189x& = & 70-90 \\\Leftrightarrow & \color{red}{-189} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-189} & & \\\Leftrightarrow & x = \frac{20}{189} & & \\ & V = \left\{ \frac{20}{189} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{4}{3})& = & 7x+\frac{5}{4} \\\Leftrightarrow & -10x-\frac{8}{3}& = & 7x+\frac{5}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-120}{ \color{blue}{12} }x- \frac{32}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{15}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -120x \color{red}{-32} & = & \color{red}{84x} +15 \\\Leftrightarrow & -120x \color{red}{-32} \color{blue}{+32} \color{blue}{-84x} & = & \color{red}{84x} +15 \color{blue}{-84x} \color{blue}{+32} \\\Leftrightarrow & -120x-84x& = & 15+32 \\\Leftrightarrow & \color{red}{-204} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-204} & & \\\Leftrightarrow & x = \frac{-47}{204} & & \\ & V = \left\{ \frac{-47}{204} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{5}{4})& = & 4x+\frac{8}{5} \\\Leftrightarrow & -15x+\frac{25}{4}& = & 4x+\frac{8}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-300}{ \color{blue}{20} }x+ \frac{125}{ \color{blue}{20} })& = & (\frac{80}{ \color{blue}{20} }x+ \frac{32}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -300x \color{red}{+125} & = & \color{red}{80x} +32 \\\Leftrightarrow & -300x \color{red}{+125} \color{blue}{-125} \color{blue}{-80x} & = & \color{red}{80x} +32 \color{blue}{-80x} \color{blue}{-125} \\\Leftrightarrow & -300x-80x& = & 32-125 \\\Leftrightarrow & \color{red}{-380} x& = & -93 \\\Leftrightarrow & x = \frac{-93}{-380} & & \\\Leftrightarrow & x = \frac{93}{380} & & \\ & V = \left\{ \frac{93}{380} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{3}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -9x+\frac{9}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-45}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -45x \color{red}{+9} & = & \color{red}{25x} +6 \\\Leftrightarrow & -45x \color{red}{+9} \color{blue}{-9} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{-9} \\\Leftrightarrow & -45x-25x& = & 6-9 \\\Leftrightarrow & \color{red}{-70} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-70} & & \\\Leftrightarrow & x = \frac{3}{70} & & \\ & V = \left\{ \frac{3}{70} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{3}{11})& = & 5x+\frac{2}{9} \\\Leftrightarrow & 12x-\frac{18}{11}& = & 5x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1188}{ \color{blue}{99} }x- \frac{162}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1188x \color{red}{-162} & = & \color{red}{495x} +22 \\\Leftrightarrow & 1188x \color{red}{-162} \color{blue}{+162} \color{blue}{-495x} & = & \color{red}{495x} +22 \color{blue}{-495x} \color{blue}{+162} \\\Leftrightarrow & 1188x-495x& = & 22+162 \\\Leftrightarrow & \color{red}{693} x& = & 184 \\\Leftrightarrow & x = \frac{184}{693} & & \\ & V = \left\{ \frac{184}{693} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{2}{3})& = & -9x+\frac{3}{2} \\\Leftrightarrow & -8x+\frac{8}{3}& = & -9x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-48}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -48x \color{red}{+16} & = & \color{red}{-54x} +9 \\\Leftrightarrow & -48x \color{red}{+16} \color{blue}{-16} \color{blue}{+54x} & = & \color{red}{-54x} +9 \color{blue}{+54x} \color{blue}{-16} \\\Leftrightarrow & -48x+54x& = & 9-16 \\\Leftrightarrow & \color{red}{6} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{6} & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{1}{3})& = & -3x+\frac{4}{7} \\\Leftrightarrow & -14x-\frac{7}{3}& = & -3x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-294}{ \color{blue}{21} }x- \frac{49}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -294x \color{red}{-49} & = & \color{red}{-63x} +12 \\\Leftrightarrow & -294x \color{red}{-49} \color{blue}{+49} \color{blue}{+63x} & = & \color{red}{-63x} +12 \color{blue}{+63x} \color{blue}{+49} \\\Leftrightarrow & -294x+63x& = & 12+49 \\\Leftrightarrow & \color{red}{-231} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-231} & & \\\Leftrightarrow & x = \frac{-61}{231} & & \\ & V = \left\{ \frac{-61}{231} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{4}{3})& = & 9x+\frac{8}{3} \\\Leftrightarrow & 10x+\frac{20}{3}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{30}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 30x \color{red}{+20} & = & \color{red}{27x} +8 \\\Leftrightarrow & 30x \color{red}{+20} \color{blue}{-20} \color{blue}{-27x} & = & \color{red}{27x} +8 \color{blue}{-27x} \color{blue}{-20} \\\Leftrightarrow & 30x-27x& = & 8-20 \\\Leftrightarrow & \color{red}{3} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{3} & & \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{2}{9})& = & 9x+\frac{7}{2} \\\Leftrightarrow & -20x-\frac{8}{9}& = & 9x+\frac{7}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-360}{ \color{blue}{18} }x- \frac{16}{ \color{blue}{18} })& = & (\frac{162}{ \color{blue}{18} }x+ \frac{63}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -360x \color{red}{-16} & = & \color{red}{162x} +63 \\\Leftrightarrow & -360x \color{red}{-16} \color{blue}{+16} \color{blue}{-162x} & = & \color{red}{162x} +63 \color{blue}{-162x} \color{blue}{+16} \\\Leftrightarrow & -360x-162x& = & 63+16 \\\Leftrightarrow & \color{red}{-522} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-522} & & \\\Leftrightarrow & x = \frac{-79}{522} & & \\ & V = \left\{ \frac{-79}{522} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{5}{7})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 10x-\frac{10}{7}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{70}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 70x \color{red}{-10} & = & \color{red}{49x} +10 \\\Leftrightarrow & 70x \color{red}{-10} \color{blue}{+10} \color{blue}{-49x} & = & \color{red}{49x} +10 \color{blue}{-49x} \color{blue}{+10} \\\Leftrightarrow & 70x-49x& = & 10+10 \\\Leftrightarrow & \color{red}{21} x& = & 20 \\\Leftrightarrow & x = \frac{20}{21} & & \\ & V = \left\{ \frac{20}{21} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{4}{3})& = & -3x+\frac{7}{8} \\\Leftrightarrow & 28x+\frac{28}{3}& = & -3x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{672}{ \color{blue}{24} }x+ \frac{224}{ \color{blue}{24} })& = & (\frac{-72}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 672x \color{red}{+224} & = & \color{red}{-72x} +21 \\\Leftrightarrow & 672x \color{red}{+224} \color{blue}{-224} \color{blue}{+72x} & = & \color{red}{-72x} +21 \color{blue}{+72x} \color{blue}{-224} \\\Leftrightarrow & 672x+72x& = & 21-224 \\\Leftrightarrow & \color{red}{744} x& = & -203 \\\Leftrightarrow & x = \frac{-203}{744} & & \\ & V = \left\{ \frac{-203}{744} \right\} & \\\end{align}\)