Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{5}{2})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 9x+\frac{15}{2}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{198}{ \color{blue}{22} }x+ \frac{165}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{12}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 198x \color{red}{+165} & = & \color{red}{110x} +12 \\\Leftrightarrow & 198x \color{red}{+165} \color{blue}{-165} \color{blue}{-110x} & = & \color{red}{110x} +12 \color{blue}{-110x} \color{blue}{-165} \\\Leftrightarrow & 198x-110x& = & 12-165 \\\Leftrightarrow & \color{red}{88} x& = & -153 \\\Leftrightarrow & x = \frac{-153}{88} & & \\ & V = \left\{ \frac{-153}{88} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{2}{3})& = & -3x+\frac{8}{5} \\\Leftrightarrow & 14x-\frac{14}{3}& = & -3x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{210}{ \color{blue}{15} }x- \frac{70}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 210x \color{red}{-70} & = & \color{red}{-45x} +24 \\\Leftrightarrow & 210x \color{red}{-70} \color{blue}{+70} \color{blue}{+45x} & = & \color{red}{-45x} +24 \color{blue}{+45x} \color{blue}{+70} \\\Leftrightarrow & 210x+45x& = & 24+70 \\\Leftrightarrow & \color{red}{255} x& = & 94 \\\Leftrightarrow & x = \frac{94}{255} & & \\ & V = \left\{ \frac{94}{255} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{2}{5})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 6x-\frac{4}{5}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{28}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-28} & = & \color{red}{-245x} +50 \\\Leftrightarrow & 210x \color{red}{-28} \color{blue}{+28} \color{blue}{+245x} & = & \color{red}{-245x} +50 \color{blue}{+245x} \color{blue}{+28} \\\Leftrightarrow & 210x+245x& = & 50+28 \\\Leftrightarrow & \color{red}{455} x& = & 78 \\\Leftrightarrow & x = \frac{78}{455} & & \\\Leftrightarrow & x = \frac{6}{35} & & \\ & V = \left\{ \frac{6}{35} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{4}{9})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -10x-\frac{8}{9}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{-8} & = & \color{red}{-63x} +30 \\\Leftrightarrow & -90x \color{red}{-8} \color{blue}{+8} \color{blue}{+63x} & = & \color{red}{-63x} +30 \color{blue}{+63x} \color{blue}{+8} \\\Leftrightarrow & -90x+63x& = & 30+8 \\\Leftrightarrow & \color{red}{-27} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-27} & & \\\Leftrightarrow & x = \frac{-38}{27} & & \\ & V = \left\{ \frac{-38}{27} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{5}{7})& = & 7x+\frac{3}{4} \\\Leftrightarrow & -10x+\frac{25}{7}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-280}{ \color{blue}{28} }x+ \frac{100}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -280x \color{red}{+100} & = & \color{red}{196x} +21 \\\Leftrightarrow & -280x \color{red}{+100} \color{blue}{-100} \color{blue}{-196x} & = & \color{red}{196x} +21 \color{blue}{-196x} \color{blue}{-100} \\\Leftrightarrow & -280x-196x& = & 21-100 \\\Leftrightarrow & \color{red}{-476} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{-476} & & \\\Leftrightarrow & x = \frac{79}{476} & & \\ & V = \left\{ \frac{79}{476} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{4}{5})& = & 5x+\frac{9}{8} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{9}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{480}{ \color{blue}{40} }x- \frac{96}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{45}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 480x \color{red}{-96} & = & \color{red}{200x} +45 \\\Leftrightarrow & 480x \color{red}{-96} \color{blue}{+96} \color{blue}{-200x} & = & \color{red}{200x} +45 \color{blue}{-200x} \color{blue}{+96} \\\Leftrightarrow & 480x-200x& = & 45+96 \\\Leftrightarrow & \color{red}{280} x& = & 141 \\\Leftrightarrow & x = \frac{141}{280} & & \\ & V = \left\{ \frac{141}{280} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{3}{4})& = & -3x+\frac{7}{2} \\\Leftrightarrow & 20x+\frac{15}{4}& = & -3x+\frac{7}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{80}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{-12}{ \color{blue}{4} }x+ \frac{14}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 80x \color{red}{+15} & = & \color{red}{-12x} +14 \\\Leftrightarrow & 80x \color{red}{+15} \color{blue}{-15} \color{blue}{+12x} & = & \color{red}{-12x} +14 \color{blue}{+12x} \color{blue}{-15} \\\Leftrightarrow & 80x+12x& = & 14-15 \\\Leftrightarrow & \color{red}{92} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{92} & & \\ & V = \left\{ \frac{-1}{92} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{2}{3})& = & 4x+\frac{8}{3} \\\Leftrightarrow & 35x-\frac{14}{3}& = & 4x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{105}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{12}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 105x \color{red}{-14} & = & \color{red}{12x} +8 \\\Leftrightarrow & 105x \color{red}{-14} \color{blue}{+14} \color{blue}{-12x} & = & \color{red}{12x} +8 \color{blue}{-12x} \color{blue}{+14} \\\Leftrightarrow & 105x-12x& = & 8+14 \\\Leftrightarrow & \color{red}{93} x& = & 22 \\\Leftrightarrow & x = \frac{22}{93} & & \\ & V = \left\{ \frac{22}{93} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{2}{3})& = & -8x+\frac{3}{2} \\\Leftrightarrow & -28x-\frac{14}{3}& = & -8x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-168}{ \color{blue}{6} }x- \frac{28}{ \color{blue}{6} })& = & (\frac{-48}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -168x \color{red}{-28} & = & \color{red}{-48x} +9 \\\Leftrightarrow & -168x \color{red}{-28} \color{blue}{+28} \color{blue}{+48x} & = & \color{red}{-48x} +9 \color{blue}{+48x} \color{blue}{+28} \\\Leftrightarrow & -168x+48x& = & 9+28 \\\Leftrightarrow & \color{red}{-120} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-120} & & \\\Leftrightarrow & x = \frac{-37}{120} & & \\ & V = \left\{ \frac{-37}{120} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{5}{11})& = & 7x+\frac{9}{4} \\\Leftrightarrow & 30x-\frac{30}{11}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1320}{ \color{blue}{44} }x- \frac{120}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1320x \color{red}{-120} & = & \color{red}{308x} +99 \\\Leftrightarrow & 1320x \color{red}{-120} \color{blue}{+120} \color{blue}{-308x} & = & \color{red}{308x} +99 \color{blue}{-308x} \color{blue}{+120} \\\Leftrightarrow & 1320x-308x& = & 99+120 \\\Leftrightarrow & \color{red}{1012} x& = & 219 \\\Leftrightarrow & x = \frac{219}{1012} & & \\ & V = \left\{ \frac{219}{1012} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{2}{5})& = & -7x+\frac{2}{7} \\\Leftrightarrow & -10x-\frac{4}{5}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x- \frac{28}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{-28} & = & \color{red}{-245x} +10 \\\Leftrightarrow & -350x \color{red}{-28} \color{blue}{+28} \color{blue}{+245x} & = & \color{red}{-245x} +10 \color{blue}{+245x} \color{blue}{+28} \\\Leftrightarrow & -350x+245x& = & 10+28 \\\Leftrightarrow & \color{red}{-105} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-105} & & \\\Leftrightarrow & x = \frac{-38}{105} & & \\ & V = \left\{ \frac{-38}{105} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{2}{5})& = & -3x+\frac{8}{5} \\\Leftrightarrow & -8x+\frac{4}{5}& = & -3x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-40}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} })& = & (\frac{-15}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -40x \color{red}{+4} & = & \color{red}{-15x} +8 \\\Leftrightarrow & -40x \color{red}{+4} \color{blue}{-4} \color{blue}{+15x} & = & \color{red}{-15x} +8 \color{blue}{+15x} \color{blue}{-4} \\\Leftrightarrow & -40x+15x& = & 8-4 \\\Leftrightarrow & \color{red}{-25} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-25} & & \\\Leftrightarrow & x = \frac{-4}{25} & & \\ & V = \left\{ \frac{-4}{25} \right\} & \\\end{align}\)