Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{5}{7})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -6x-\frac{15}{7}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x- \frac{45}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{-45} & = & \color{red}{-147x} +28 \\\Leftrightarrow & -126x \color{red}{-45} \color{blue}{+45} \color{blue}{+147x} & = & \color{red}{-147x} +28 \color{blue}{+147x} \color{blue}{+45} \\\Leftrightarrow & -126x+147x& = & 28+45 \\\Leftrightarrow & \color{red}{21} x& = & 73 \\\Leftrightarrow & x = \frac{73}{21} & & \\ & V = \left\{ \frac{73}{21} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{2}{5})& = & -3x+\frac{9}{11} \\\Leftrightarrow & 10x+\frac{4}{5}& = & -3x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{550}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 550x \color{red}{+44} & = & \color{red}{-165x} +45 \\\Leftrightarrow & 550x \color{red}{+44} \color{blue}{-44} \color{blue}{+165x} & = & \color{red}{-165x} +45 \color{blue}{+165x} \color{blue}{-44} \\\Leftrightarrow & 550x+165x& = & 45-44 \\\Leftrightarrow & \color{red}{715} x& = & 1 \\\Leftrightarrow & x = \frac{1}{715} & & \\ & V = \left\{ \frac{1}{715} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{3}{5})& = & -7x+\frac{2}{5} \\\Leftrightarrow & 6x+\frac{6}{5}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{30}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 30x \color{red}{+6} & = & \color{red}{-35x} +2 \\\Leftrightarrow & 30x \color{red}{+6} \color{blue}{-6} \color{blue}{+35x} & = & \color{red}{-35x} +2 \color{blue}{+35x} \color{blue}{-6} \\\Leftrightarrow & 30x+35x& = & 2-6 \\\Leftrightarrow & \color{red}{65} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{65} & & \\ & V = \left\{ \frac{-4}{65} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{2}{3})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 20x+\frac{8}{3}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{+56} & = & \color{red}{-147x} +30 \\\Leftrightarrow & 420x \color{red}{+56} \color{blue}{-56} \color{blue}{+147x} & = & \color{red}{-147x} +30 \color{blue}{+147x} \color{blue}{-56} \\\Leftrightarrow & 420x+147x& = & 30-56 \\\Leftrightarrow & \color{red}{567} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{567} & & \\ & V = \left\{ \frac{-26}{567} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{3}{11})& = & -3x+\frac{10}{9} \\\Leftrightarrow & -8x-\frac{12}{11}& = & -3x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-792}{ \color{blue}{99} }x- \frac{108}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -792x \color{red}{-108} & = & \color{red}{-297x} +110 \\\Leftrightarrow & -792x \color{red}{-108} \color{blue}{+108} \color{blue}{+297x} & = & \color{red}{-297x} +110 \color{blue}{+297x} \color{blue}{+108} \\\Leftrightarrow & -792x+297x& = & 110+108 \\\Leftrightarrow & \color{red}{-495} x& = & 218 \\\Leftrightarrow & x = \frac{218}{-495} & & \\\Leftrightarrow & x = \frac{-218}{495} & & \\ & V = \left\{ \frac{-218}{495} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{2}{3})& = & -5x+\frac{5}{7} \\\Leftrightarrow & -12x-\frac{8}{3}& = & -5x+\frac{5}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{15}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{-56} & = & \color{red}{-105x} +15 \\\Leftrightarrow & -252x \color{red}{-56} \color{blue}{+56} \color{blue}{+105x} & = & \color{red}{-105x} +15 \color{blue}{+105x} \color{blue}{+56} \\\Leftrightarrow & -252x+105x& = & 15+56 \\\Leftrightarrow & \color{red}{-147} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-147} & & \\\Leftrightarrow & x = \frac{-71}{147} & & \\ & V = \left\{ \frac{-71}{147} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{3}{11})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -30x-\frac{18}{11}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-330}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -330x \color{red}{-18} & = & \color{red}{77x} +6 \\\Leftrightarrow & -330x \color{red}{-18} \color{blue}{+18} \color{blue}{-77x} & = & \color{red}{77x} +6 \color{blue}{-77x} \color{blue}{+18} \\\Leftrightarrow & -330x-77x& = & 6+18 \\\Leftrightarrow & \color{red}{-407} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-407} & & \\\Leftrightarrow & x = \frac{-24}{407} & & \\ & V = \left\{ \frac{-24}{407} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{5}{7})& = & 3x+\frac{9}{10} \\\Leftrightarrow & 4x+\frac{10}{7}& = & 3x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{280}{ \color{blue}{70} }x+ \frac{100}{ \color{blue}{70} })& = & (\frac{210}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 280x \color{red}{+100} & = & \color{red}{210x} +63 \\\Leftrightarrow & 280x \color{red}{+100} \color{blue}{-100} \color{blue}{-210x} & = & \color{red}{210x} +63 \color{blue}{-210x} \color{blue}{-100} \\\Leftrightarrow & 280x-210x& = & 63-100 \\\Leftrightarrow & \color{red}{70} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{70} & & \\ & V = \left\{ \frac{-37}{70} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{2}{7})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -12x-\frac{6}{7}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{-18} & = & \color{red}{-105x} +28 \\\Leftrightarrow & -252x \color{red}{-18} \color{blue}{+18} \color{blue}{+105x} & = & \color{red}{-105x} +28 \color{blue}{+105x} \color{blue}{+18} \\\Leftrightarrow & -252x+105x& = & 28+18 \\\Leftrightarrow & \color{red}{-147} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-147} & & \\\Leftrightarrow & x = \frac{-46}{147} & & \\ & V = \left\{ \frac{-46}{147} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{3}{5})& = & -9x+\frac{7}{6} \\\Leftrightarrow & 8x+\frac{12}{5}& = & -9x+\frac{7}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{240}{ \color{blue}{30} }x+ \frac{72}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{35}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 240x \color{red}{+72} & = & \color{red}{-270x} +35 \\\Leftrightarrow & 240x \color{red}{+72} \color{blue}{-72} \color{blue}{+270x} & = & \color{red}{-270x} +35 \color{blue}{+270x} \color{blue}{-72} \\\Leftrightarrow & 240x+270x& = & 35-72 \\\Leftrightarrow & \color{red}{510} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{510} & & \\ & V = \left\{ \frac{-37}{510} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{2}{11})& = & -4x+\frac{7}{8} \\\Leftrightarrow & 21x+\frac{14}{11}& = & -4x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1848}{ \color{blue}{88} }x+ \frac{112}{ \color{blue}{88} })& = & (\frac{-352}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1848x \color{red}{+112} & = & \color{red}{-352x} +77 \\\Leftrightarrow & 1848x \color{red}{+112} \color{blue}{-112} \color{blue}{+352x} & = & \color{red}{-352x} +77 \color{blue}{+352x} \color{blue}{-112} \\\Leftrightarrow & 1848x+352x& = & 77-112 \\\Leftrightarrow & \color{red}{2200} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{2200} & & \\\Leftrightarrow & x = \frac{-7}{440} & & \\ & V = \left\{ \frac{-7}{440} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{2}{3})& = & 9x+\frac{9}{2} \\\Leftrightarrow & -8x-\frac{8}{3}& = & 9x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-48}{ \color{blue}{6} }x- \frac{16}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -48x \color{red}{-16} & = & \color{red}{54x} +27 \\\Leftrightarrow & -48x \color{red}{-16} \color{blue}{+16} \color{blue}{-54x} & = & \color{red}{54x} +27 \color{blue}{-54x} \color{blue}{+16} \\\Leftrightarrow & -48x-54x& = & 27+16 \\\Leftrightarrow & \color{red}{-102} x& = & 43 \\\Leftrightarrow & x = \frac{43}{-102} & & \\\Leftrightarrow & x = \frac{-43}{102} & & \\ & V = \left\{ \frac{-43}{102} \right\} & \\\end{align}\)