Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{2}{9})& = & 7x+\frac{9}{2} \\\Leftrightarrow & -10x-\frac{4}{9}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-180}{ \color{blue}{18} }x- \frac{8}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -180x \color{red}{-8} & = & \color{red}{126x} +81 \\\Leftrightarrow & -180x \color{red}{-8} \color{blue}{+8} \color{blue}{-126x} & = & \color{red}{126x} +81 \color{blue}{-126x} \color{blue}{+8} \\\Leftrightarrow & -180x-126x& = & 81+8 \\\Leftrightarrow & \color{red}{-306} x& = & 89 \\\Leftrightarrow & x = \frac{89}{-306} & & \\\Leftrightarrow & x = \frac{-89}{306} & & \\ & V = \left\{ \frac{-89}{306} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{5}{7})& = & -5x+\frac{10}{7} \\\Leftrightarrow & -24x-\frac{30}{7}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-168}{ \color{blue}{7} }x- \frac{30}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -168x \color{red}{-30} & = & \color{red}{-35x} +10 \\\Leftrightarrow & -168x \color{red}{-30} \color{blue}{+30} \color{blue}{+35x} & = & \color{red}{-35x} +10 \color{blue}{+35x} \color{blue}{+30} \\\Leftrightarrow & -168x+35x& = & 10+30 \\\Leftrightarrow & \color{red}{-133} x& = & 40 \\\Leftrightarrow & x = \frac{40}{-133} & & \\\Leftrightarrow & x = \frac{-40}{133} & & \\ & V = \left\{ \frac{-40}{133} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{2}{5})& = & -7x+\frac{2}{7} \\\Leftrightarrow & 18x+\frac{12}{5}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{+84} & = & \color{red}{-245x} +10 \\\Leftrightarrow & 630x \color{red}{+84} \color{blue}{-84} \color{blue}{+245x} & = & \color{red}{-245x} +10 \color{blue}{+245x} \color{blue}{-84} \\\Leftrightarrow & 630x+245x& = & 10-84 \\\Leftrightarrow & \color{red}{875} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{875} & & \\ & V = \left\{ \frac{-74}{875} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{4}{7})& = & 5x+\frac{7}{12} \\\Leftrightarrow & -12x+\frac{12}{7}& = & 5x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-1008}{ \color{blue}{84} }x+ \frac{144}{ \color{blue}{84} })& = & (\frac{420}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -1008x \color{red}{+144} & = & \color{red}{420x} +49 \\\Leftrightarrow & -1008x \color{red}{+144} \color{blue}{-144} \color{blue}{-420x} & = & \color{red}{420x} +49 \color{blue}{-420x} \color{blue}{-144} \\\Leftrightarrow & -1008x-420x& = & 49-144 \\\Leftrightarrow & \color{red}{-1428} x& = & -95 \\\Leftrightarrow & x = \frac{-95}{-1428} & & \\\Leftrightarrow & x = \frac{95}{1428} & & \\ & V = \left\{ \frac{95}{1428} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{7})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -20x-\frac{16}{7}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x- \frac{176}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{-176} & = & \color{red}{539x} +42 \\\Leftrightarrow & -1540x \color{red}{-176} \color{blue}{+176} \color{blue}{-539x} & = & \color{red}{539x} +42 \color{blue}{-539x} \color{blue}{+176} \\\Leftrightarrow & -1540x-539x& = & 42+176 \\\Leftrightarrow & \color{red}{-2079} x& = & 218 \\\Leftrightarrow & x = \frac{218}{-2079} & & \\\Leftrightarrow & x = \frac{-218}{2079} & & \\ & V = \left\{ \frac{-218}{2079} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{3}{7})& = & 3x+\frac{5}{2} \\\Leftrightarrow & 8x+\frac{6}{7}& = & 3x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{112}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{42}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 112x \color{red}{+12} & = & \color{red}{42x} +35 \\\Leftrightarrow & 112x \color{red}{+12} \color{blue}{-12} \color{blue}{-42x} & = & \color{red}{42x} +35 \color{blue}{-42x} \color{blue}{-12} \\\Leftrightarrow & 112x-42x& = & 35-12 \\\Leftrightarrow & \color{red}{70} x& = & 23 \\\Leftrightarrow & x = \frac{23}{70} & & \\ & V = \left\{ \frac{23}{70} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{5}{4})& = & -7x+\frac{8}{7} \\\Leftrightarrow & 9x+\frac{15}{4}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{252}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{32}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 252x \color{red}{+105} & = & \color{red}{-196x} +32 \\\Leftrightarrow & 252x \color{red}{+105} \color{blue}{-105} \color{blue}{+196x} & = & \color{red}{-196x} +32 \color{blue}{+196x} \color{blue}{-105} \\\Leftrightarrow & 252x+196x& = & 32-105 \\\Leftrightarrow & \color{red}{448} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{448} & & \\ & V = \left\{ \frac{-73}{448} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{4}{3})& = & -3x+\frac{4}{3} \\\Leftrightarrow & -8x-\frac{8}{3}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-24}{ \color{blue}{3} }x- \frac{8}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -24x \color{red}{-8} & = & \color{red}{-9x} +4 \\\Leftrightarrow & -24x \color{red}{-8} \color{blue}{+8} \color{blue}{+9x} & = & \color{red}{-9x} +4 \color{blue}{+9x} \color{blue}{+8} \\\Leftrightarrow & -24x+9x& = & 4+8 \\\Leftrightarrow & \color{red}{-15} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-15} & & \\\Leftrightarrow & x = \frac{-4}{5} & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{3}{4})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 25x+\frac{15}{4}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{100}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{-28}{ \color{blue}{4} }x+ \frac{6}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 100x \color{red}{+15} & = & \color{red}{-28x} +6 \\\Leftrightarrow & 100x \color{red}{+15} \color{blue}{-15} \color{blue}{+28x} & = & \color{red}{-28x} +6 \color{blue}{+28x} \color{blue}{-15} \\\Leftrightarrow & 100x+28x& = & 6-15 \\\Leftrightarrow & \color{red}{128} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{128} & & \\ & V = \left\{ \frac{-9}{128} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{4}{7})& = & -3x+\frac{2}{9} \\\Leftrightarrow & 8x-\frac{16}{7}& = & -3x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x- \frac{144}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{-144} & = & \color{red}{-189x} +14 \\\Leftrightarrow & 504x \color{red}{-144} \color{blue}{+144} \color{blue}{+189x} & = & \color{red}{-189x} +14 \color{blue}{+189x} \color{blue}{+144} \\\Leftrightarrow & 504x+189x& = & 14+144 \\\Leftrightarrow & \color{red}{693} x& = & 158 \\\Leftrightarrow & x = \frac{158}{693} & & \\ & V = \left\{ \frac{158}{693} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{8})& = & -7x+\frac{5}{2} \\\Leftrightarrow & 10x-\frac{25}{8}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{80}{ \color{blue}{8} }x- \frac{25}{ \color{blue}{8} })& = & (\frac{-56}{ \color{blue}{8} }x+ \frac{20}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 80x \color{red}{-25} & = & \color{red}{-56x} +20 \\\Leftrightarrow & 80x \color{red}{-25} \color{blue}{+25} \color{blue}{+56x} & = & \color{red}{-56x} +20 \color{blue}{+56x} \color{blue}{+25} \\\Leftrightarrow & 80x+56x& = & 20+25 \\\Leftrightarrow & \color{red}{136} x& = & 45 \\\Leftrightarrow & x = \frac{45}{136} & & \\ & V = \left\{ \frac{45}{136} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{4}{11})& = & 3x+\frac{9}{2} \\\Leftrightarrow & -14x-\frac{28}{11}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-308}{ \color{blue}{22} }x- \frac{56}{ \color{blue}{22} })& = & (\frac{66}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -308x \color{red}{-56} & = & \color{red}{66x} +99 \\\Leftrightarrow & -308x \color{red}{-56} \color{blue}{+56} \color{blue}{-66x} & = & \color{red}{66x} +99 \color{blue}{-66x} \color{blue}{+56} \\\Leftrightarrow & -308x-66x& = & 99+56 \\\Leftrightarrow & \color{red}{-374} x& = & 155 \\\Leftrightarrow & x = \frac{155}{-374} & & \\\Leftrightarrow & x = \frac{-155}{374} & & \\ & V = \left\{ \frac{-155}{374} \right\} & \\\end{align}\)