Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{3}{8})& = & -8x+\frac{3}{10} \\\Leftrightarrow & 21x+\frac{21}{8}& = & -8x+\frac{3}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{840}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{-320}{ \color{blue}{40} }x+ \frac{12}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 840x \color{red}{+105} & = & \color{red}{-320x} +12 \\\Leftrightarrow & 840x \color{red}{+105} \color{blue}{-105} \color{blue}{+320x} & = & \color{red}{-320x} +12 \color{blue}{+320x} \color{blue}{-105} \\\Leftrightarrow & 840x+320x& = & 12-105 \\\Leftrightarrow & \color{red}{1160} x& = & -93 \\\Leftrightarrow & x = \frac{-93}{1160} & & \\ & V = \left\{ \frac{-93}{1160} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{5}{2})& = & -9x+\frac{9}{2} \\\Leftrightarrow & 28x-\frac{35}{2}& = & -9x+\frac{9}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{56}{ \color{blue}{2} }x- \frac{35}{ \color{blue}{2} })& = & (\frac{-18}{ \color{blue}{2} }x+ \frac{9}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 56x \color{red}{-35} & = & \color{red}{-18x} +9 \\\Leftrightarrow & 56x \color{red}{-35} \color{blue}{+35} \color{blue}{+18x} & = & \color{red}{-18x} +9 \color{blue}{+18x} \color{blue}{+35} \\\Leftrightarrow & 56x+18x& = & 9+35 \\\Leftrightarrow & \color{red}{74} x& = & 44 \\\Leftrightarrow & x = \frac{44}{74} & & \\\Leftrightarrow & x = \frac{22}{37} & & \\ & V = \left\{ \frac{22}{37} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{8})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 21x-\frac{21}{8}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{504}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{120}{ \color{blue}{24} }x+ \frac{16}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 504x \color{red}{-63} & = & \color{red}{120x} +16 \\\Leftrightarrow & 504x \color{red}{-63} \color{blue}{+63} \color{blue}{-120x} & = & \color{red}{120x} +16 \color{blue}{-120x} \color{blue}{+63} \\\Leftrightarrow & 504x-120x& = & 16+63 \\\Leftrightarrow & \color{red}{384} x& = & 79 \\\Leftrightarrow & x = \frac{79}{384} & & \\ & V = \left\{ \frac{79}{384} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{3}{5})& = & -3x+\frac{4}{3} \\\Leftrightarrow & -18x-\frac{18}{5}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-270}{ \color{blue}{15} }x- \frac{54}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -270x \color{red}{-54} & = & \color{red}{-45x} +20 \\\Leftrightarrow & -270x \color{red}{-54} \color{blue}{+54} \color{blue}{+45x} & = & \color{red}{-45x} +20 \color{blue}{+45x} \color{blue}{+54} \\\Leftrightarrow & -270x+45x& = & 20+54 \\\Leftrightarrow & \color{red}{-225} x& = & 74 \\\Leftrightarrow & x = \frac{74}{-225} & & \\\Leftrightarrow & x = \frac{-74}{225} & & \\ & V = \left\{ \frac{-74}{225} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{2}{7})& = & 3x+\frac{4}{9} \\\Leftrightarrow & 10x+\frac{10}{7}& = & 3x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{630}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 630x \color{red}{+90} & = & \color{red}{189x} +28 \\\Leftrightarrow & 630x \color{red}{+90} \color{blue}{-90} \color{blue}{-189x} & = & \color{red}{189x} +28 \color{blue}{-189x} \color{blue}{-90} \\\Leftrightarrow & 630x-189x& = & 28-90 \\\Leftrightarrow & \color{red}{441} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{441} & & \\ & V = \left\{ \frac{-62}{441} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+1)& = & -9x+\frac{9}{2} \\\Leftrightarrow & 20x-5& = & -9x+\frac{9}{2} \\ & & & \text{kgv van noemers 1 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{40}{ \color{blue}{2} }x- \frac{10}{ \color{blue}{2} })& = & (\frac{-18}{ \color{blue}{2} }x+ \frac{9}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 40x \color{red}{-10} & = & \color{red}{-18x} +9 \\\Leftrightarrow & 40x \color{red}{-10} \color{blue}{+10} \color{blue}{+18x} & = & \color{red}{-18x} +9 \color{blue}{+18x} \color{blue}{+10} \\\Leftrightarrow & 40x+18x& = & 9+10 \\\Leftrightarrow & \color{red}{58} x& = & 19 \\\Leftrightarrow & x = \frac{19}{58} & & \\ & V = \left\{ \frac{19}{58} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{5})& = & 9x+\frac{10}{7} \\\Leftrightarrow & -8x+\frac{8}{5}& = & 9x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{+56} & = & \color{red}{315x} +50 \\\Leftrightarrow & -280x \color{red}{+56} \color{blue}{-56} \color{blue}{-315x} & = & \color{red}{315x} +50 \color{blue}{-315x} \color{blue}{-56} \\\Leftrightarrow & -280x-315x& = & 50-56 \\\Leftrightarrow & \color{red}{-595} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-595} & & \\\Leftrightarrow & x = \frac{6}{595} & & \\ & V = \left\{ \frac{6}{595} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{3}{4})& = & 3x+\frac{8}{7} \\\Leftrightarrow & 14x-\frac{21}{4}& = & 3x+\frac{8}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{392}{ \color{blue}{28} }x- \frac{147}{ \color{blue}{28} })& = & (\frac{84}{ \color{blue}{28} }x+ \frac{32}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 392x \color{red}{-147} & = & \color{red}{84x} +32 \\\Leftrightarrow & 392x \color{red}{-147} \color{blue}{+147} \color{blue}{-84x} & = & \color{red}{84x} +32 \color{blue}{-84x} \color{blue}{+147} \\\Leftrightarrow & 392x-84x& = & 32+147 \\\Leftrightarrow & \color{red}{308} x& = & 179 \\\Leftrightarrow & x = \frac{179}{308} & & \\ & V = \left\{ \frac{179}{308} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{4}{7})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -4x+\frac{8}{7}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-140}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -140x \color{red}{+40} & = & \color{red}{-175x} +42 \\\Leftrightarrow & -140x \color{red}{+40} \color{blue}{-40} \color{blue}{+175x} & = & \color{red}{-175x} +42 \color{blue}{+175x} \color{blue}{-40} \\\Leftrightarrow & -140x+175x& = & 42-40 \\\Leftrightarrow & \color{red}{35} x& = & 2 \\\Leftrightarrow & x = \frac{2}{35} & & \\ & V = \left\{ \frac{2}{35} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{3}{11})& = & -7x+\frac{4}{5} \\\Leftrightarrow & 10x-\frac{6}{11}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{550}{ \color{blue}{55} }x- \frac{30}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 550x \color{red}{-30} & = & \color{red}{-385x} +44 \\\Leftrightarrow & 550x \color{red}{-30} \color{blue}{+30} \color{blue}{+385x} & = & \color{red}{-385x} +44 \color{blue}{+385x} \color{blue}{+30} \\\Leftrightarrow & 550x+385x& = & 44+30 \\\Leftrightarrow & \color{red}{935} x& = & 74 \\\Leftrightarrow & x = \frac{74}{935} & & \\ & V = \left\{ \frac{74}{935} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{5}{4})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -6x-\frac{15}{4}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-24}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{28}{ \color{blue}{4} }x+ \frac{6}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -24x \color{red}{-15} & = & \color{red}{28x} +6 \\\Leftrightarrow & -24x \color{red}{-15} \color{blue}{+15} \color{blue}{-28x} & = & \color{red}{28x} +6 \color{blue}{-28x} \color{blue}{+15} \\\Leftrightarrow & -24x-28x& = & 6+15 \\\Leftrightarrow & \color{red}{-52} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-52} & & \\\Leftrightarrow & x = \frac{-21}{52} & & \\ & V = \left\{ \frac{-21}{52} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{3}{4})& = & -7x+\frac{4}{7} \\\Leftrightarrow & 12x+\frac{9}{4}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{336}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{16}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 336x \color{red}{+63} & = & \color{red}{-196x} +16 \\\Leftrightarrow & 336x \color{red}{+63} \color{blue}{-63} \color{blue}{+196x} & = & \color{red}{-196x} +16 \color{blue}{+196x} \color{blue}{-63} \\\Leftrightarrow & 336x+196x& = & 16-63 \\\Leftrightarrow & \color{red}{532} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{532} & & \\ & V = \left\{ \frac{-47}{532} \right\} & \\\end{align}\)