Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{2}{7})& = & -2x+\frac{10}{7} \\\Leftrightarrow & 15x+\frac{6}{7}& = & -2x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{105}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-14}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 105x \color{red}{+6} & = & \color{red}{-14x} +10 \\\Leftrightarrow & 105x \color{red}{+6} \color{blue}{-6} \color{blue}{+14x} & = & \color{red}{-14x} +10 \color{blue}{+14x} \color{blue}{-6} \\\Leftrightarrow & 105x+14x& = & 10-6 \\\Leftrightarrow & \color{red}{119} x& = & 4 \\\Leftrightarrow & x = \frac{4}{119} & & \\ & V = \left\{ \frac{4}{119} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{4}{5})& = & 8x+\frac{6}{5} \\\Leftrightarrow & -21x-\frac{28}{5}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-105}{ \color{blue}{5} }x- \frac{28}{ \color{blue}{5} })& = & (\frac{40}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -105x \color{red}{-28} & = & \color{red}{40x} +6 \\\Leftrightarrow & -105x \color{red}{-28} \color{blue}{+28} \color{blue}{-40x} & = & \color{red}{40x} +6 \color{blue}{-40x} \color{blue}{+28} \\\Leftrightarrow & -105x-40x& = & 6+28 \\\Leftrightarrow & \color{red}{-145} x& = & 34 \\\Leftrightarrow & x = \frac{34}{-145} & & \\\Leftrightarrow & x = \frac{-34}{145} & & \\ & V = \left\{ \frac{-34}{145} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{5}{9})& = & 8x+\frac{5}{2} \\\Leftrightarrow & -21x-\frac{35}{9}& = & 8x+\frac{5}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-378}{ \color{blue}{18} }x- \frac{70}{ \color{blue}{18} })& = & (\frac{144}{ \color{blue}{18} }x+ \frac{45}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -378x \color{red}{-70} & = & \color{red}{144x} +45 \\\Leftrightarrow & -378x \color{red}{-70} \color{blue}{+70} \color{blue}{-144x} & = & \color{red}{144x} +45 \color{blue}{-144x} \color{blue}{+70} \\\Leftrightarrow & -378x-144x& = & 45+70 \\\Leftrightarrow & \color{red}{-522} x& = & 115 \\\Leftrightarrow & x = \frac{115}{-522} & & \\\Leftrightarrow & x = \frac{-115}{522} & & \\ & V = \left\{ \frac{-115}{522} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{2}{3})& = & 9x+\frac{5}{2} \\\Leftrightarrow & 28x+\frac{14}{3}& = & 9x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{168}{ \color{blue}{6} }x+ \frac{28}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 168x \color{red}{+28} & = & \color{red}{54x} +15 \\\Leftrightarrow & 168x \color{red}{+28} \color{blue}{-28} \color{blue}{-54x} & = & \color{red}{54x} +15 \color{blue}{-54x} \color{blue}{-28} \\\Leftrightarrow & 168x-54x& = & 15-28 \\\Leftrightarrow & \color{red}{114} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{114} & & \\ & V = \left\{ \frac{-13}{114} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{3}{7})& = & -9x+\frac{8}{5} \\\Leftrightarrow & -8x-\frac{6}{7}& = & -9x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{-30} & = & \color{red}{-315x} +56 \\\Leftrightarrow & -280x \color{red}{-30} \color{blue}{+30} \color{blue}{+315x} & = & \color{red}{-315x} +56 \color{blue}{+315x} \color{blue}{+30} \\\Leftrightarrow & -280x+315x& = & 56+30 \\\Leftrightarrow & \color{red}{35} x& = & 86 \\\Leftrightarrow & x = \frac{86}{35} & & \\ & V = \left\{ \frac{86}{35} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{9})& = & -3x+\frac{10}{7} \\\Leftrightarrow & -8x+\frac{8}{9}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-504}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -504x \color{red}{+56} & = & \color{red}{-189x} +90 \\\Leftrightarrow & -504x \color{red}{+56} \color{blue}{-56} \color{blue}{+189x} & = & \color{red}{-189x} +90 \color{blue}{+189x} \color{blue}{-56} \\\Leftrightarrow & -504x+189x& = & 90-56 \\\Leftrightarrow & \color{red}{-315} x& = & 34 \\\Leftrightarrow & x = \frac{34}{-315} & & \\\Leftrightarrow & x = \frac{-34}{315} & & \\ & V = \left\{ \frac{-34}{315} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{2}{3})& = & -5x+\frac{5}{11} \\\Leftrightarrow & 12x-\frac{8}{3}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{-88} & = & \color{red}{-165x} +15 \\\Leftrightarrow & 396x \color{red}{-88} \color{blue}{+88} \color{blue}{+165x} & = & \color{red}{-165x} +15 \color{blue}{+165x} \color{blue}{+88} \\\Leftrightarrow & 396x+165x& = & 15+88 \\\Leftrightarrow & \color{red}{561} x& = & 103 \\\Leftrightarrow & x = \frac{103}{561} & & \\ & V = \left\{ \frac{103}{561} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{5}{3})& = & 2x+\frac{10}{3} \\\Leftrightarrow & 21x+\frac{35}{3}& = & 2x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{63}{ \color{blue}{3} }x+ \frac{35}{ \color{blue}{3} })& = & (\frac{6}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 63x \color{red}{+35} & = & \color{red}{6x} +10 \\\Leftrightarrow & 63x \color{red}{+35} \color{blue}{-35} \color{blue}{-6x} & = & \color{red}{6x} +10 \color{blue}{-6x} \color{blue}{-35} \\\Leftrightarrow & 63x-6x& = & 10-35 \\\Leftrightarrow & \color{red}{57} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{57} & & \\ & V = \left\{ \frac{-25}{57} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{3}{7})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 30x-\frac{18}{7}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{630}{ \color{blue}{21} }x- \frac{54}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 630x \color{red}{-54} & = & \color{red}{147x} +28 \\\Leftrightarrow & 630x \color{red}{-54} \color{blue}{+54} \color{blue}{-147x} & = & \color{red}{147x} +28 \color{blue}{-147x} \color{blue}{+54} \\\Leftrightarrow & 630x-147x& = & 28+54 \\\Leftrightarrow & \color{red}{483} x& = & 82 \\\Leftrightarrow & x = \frac{82}{483} & & \\ & V = \left\{ \frac{82}{483} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{5}{11})& = & 6x+\frac{3}{7} \\\Leftrightarrow & -18x-\frac{30}{11}& = & 6x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1386}{ \color{blue}{77} }x- \frac{210}{ \color{blue}{77} })& = & (\frac{462}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1386x \color{red}{-210} & = & \color{red}{462x} +33 \\\Leftrightarrow & -1386x \color{red}{-210} \color{blue}{+210} \color{blue}{-462x} & = & \color{red}{462x} +33 \color{blue}{-462x} \color{blue}{+210} \\\Leftrightarrow & -1386x-462x& = & 33+210 \\\Leftrightarrow & \color{red}{-1848} x& = & 243 \\\Leftrightarrow & x = \frac{243}{-1848} & & \\\Leftrightarrow & x = \frac{-81}{616} & & \\ & V = \left\{ \frac{-81}{616} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{2}{3})& = & 8x+\frac{8}{3} \\\Leftrightarrow & -21x+\frac{14}{3}& = & 8x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-63}{ \color{blue}{3} }x+ \frac{14}{ \color{blue}{3} })& = & (\frac{24}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -63x \color{red}{+14} & = & \color{red}{24x} +8 \\\Leftrightarrow & -63x \color{red}{+14} \color{blue}{-14} \color{blue}{-24x} & = & \color{red}{24x} +8 \color{blue}{-24x} \color{blue}{-14} \\\Leftrightarrow & -63x-24x& = & 8-14 \\\Leftrightarrow & \color{red}{-87} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-87} & & \\\Leftrightarrow & x = \frac{2}{29} & & \\ & V = \left\{ \frac{2}{29} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{3})& = & 7x+\frac{7}{2} \\\Leftrightarrow & -6x+\frac{10}{3}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-36}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -36x \color{red}{+20} & = & \color{red}{42x} +21 \\\Leftrightarrow & -36x \color{red}{+20} \color{blue}{-20} \color{blue}{-42x} & = & \color{red}{42x} +21 \color{blue}{-42x} \color{blue}{-20} \\\Leftrightarrow & -36x-42x& = & 21-20 \\\Leftrightarrow & \color{red}{-78} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-78} & & \\\Leftrightarrow & x = \frac{-1}{78} & & \\ & V = \left\{ \frac{-1}{78} \right\} & \\\end{align}\)