Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{5}{8})& = & -4x+\frac{6}{5} \\\Leftrightarrow & -15x-\frac{25}{8}& = & -4x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-600}{ \color{blue}{40} }x- \frac{125}{ \color{blue}{40} })& = & (\frac{-160}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -600x \color{red}{-125} & = & \color{red}{-160x} +48 \\\Leftrightarrow & -600x \color{red}{-125} \color{blue}{+125} \color{blue}{+160x} & = & \color{red}{-160x} +48 \color{blue}{+160x} \color{blue}{+125} \\\Leftrightarrow & -600x+160x& = & 48+125 \\\Leftrightarrow & \color{red}{-440} x& = & 173 \\\Leftrightarrow & x = \frac{173}{-440} & & \\\Leftrightarrow & x = \frac{-173}{440} & & \\ & V = \left\{ \frac{-173}{440} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{2}{3})& = & -4x+\frac{9}{10} \\\Leftrightarrow & 21x+\frac{14}{3}& = & -4x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{630}{ \color{blue}{30} }x+ \frac{140}{ \color{blue}{30} })& = & (\frac{-120}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 630x \color{red}{+140} & = & \color{red}{-120x} +27 \\\Leftrightarrow & 630x \color{red}{+140} \color{blue}{-140} \color{blue}{+120x} & = & \color{red}{-120x} +27 \color{blue}{+120x} \color{blue}{-140} \\\Leftrightarrow & 630x+120x& = & 27-140 \\\Leftrightarrow & \color{red}{750} x& = & -113 \\\Leftrightarrow & x = \frac{-113}{750} & & \\ & V = \left\{ \frac{-113}{750} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{2}{5})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 24x-\frac{12}{5}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{-132} & = & \color{red}{-275x} +30 \\\Leftrightarrow & 1320x \color{red}{-132} \color{blue}{+132} \color{blue}{+275x} & = & \color{red}{-275x} +30 \color{blue}{+275x} \color{blue}{+132} \\\Leftrightarrow & 1320x+275x& = & 30+132 \\\Leftrightarrow & \color{red}{1595} x& = & 162 \\\Leftrightarrow & x = \frac{162}{1595} & & \\ & V = \left\{ \frac{162}{1595} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{2}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -9x+\frac{6}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-45}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -45x \color{red}{+6} & = & \color{red}{25x} +6 \\\Leftrightarrow & -45x \color{red}{+6} \color{blue}{-6} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{-6} \\\Leftrightarrow & -45x-25x& = & 6-6 \\\Leftrightarrow & \color{red}{-70} x& = & 0 \\\Leftrightarrow & x = \frac{0}{-70} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{5}{11})& = & -7x+\frac{3}{4} \\\Leftrightarrow & -30x+\frac{30}{11}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1320}{ \color{blue}{44} }x+ \frac{120}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1320x \color{red}{+120} & = & \color{red}{-308x} +33 \\\Leftrightarrow & -1320x \color{red}{+120} \color{blue}{-120} \color{blue}{+308x} & = & \color{red}{-308x} +33 \color{blue}{+308x} \color{blue}{-120} \\\Leftrightarrow & -1320x+308x& = & 33-120 \\\Leftrightarrow & \color{red}{-1012} x& = & -87 \\\Leftrightarrow & x = \frac{-87}{-1012} & & \\\Leftrightarrow & x = \frac{87}{1012} & & \\ & V = \left\{ \frac{87}{1012} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{3}{5})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 20x+\frac{12}{5}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{300}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 300x \color{red}{+36} & = & \color{red}{105x} +20 \\\Leftrightarrow & 300x \color{red}{+36} \color{blue}{-36} \color{blue}{-105x} & = & \color{red}{105x} +20 \color{blue}{-105x} \color{blue}{-36} \\\Leftrightarrow & 300x-105x& = & 20-36 \\\Leftrightarrow & \color{red}{195} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{195} & & \\ & V = \left\{ \frac{-16}{195} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{2}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 8x+\frac{8}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{+40} & = & \color{red}{-385x} +66 \\\Leftrightarrow & 440x \color{red}{+40} \color{blue}{-40} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{-40} \\\Leftrightarrow & 440x+385x& = & 66-40 \\\Leftrightarrow & \color{red}{825} x& = & 26 \\\Leftrightarrow & x = \frac{26}{825} & & \\ & V = \left\{ \frac{26}{825} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{11})& = & 5x+\frac{2}{11} \\\Leftrightarrow & -4x+\frac{4}{11}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-44}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -44x \color{red}{+4} & = & \color{red}{55x} +2 \\\Leftrightarrow & -44x \color{red}{+4} \color{blue}{-4} \color{blue}{-55x} & = & \color{red}{55x} +2 \color{blue}{-55x} \color{blue}{-4} \\\Leftrightarrow & -44x-55x& = & 2-4 \\\Leftrightarrow & \color{red}{-99} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-99} & & \\\Leftrightarrow & x = \frac{2}{99} & & \\ & V = \left\{ \frac{2}{99} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{5}{4})& = & 7x+\frac{5}{2} \\\Leftrightarrow & -6x-\frac{15}{4}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-24}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{28}{ \color{blue}{4} }x+ \frac{10}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -24x \color{red}{-15} & = & \color{red}{28x} +10 \\\Leftrightarrow & -24x \color{red}{-15} \color{blue}{+15} \color{blue}{-28x} & = & \color{red}{28x} +10 \color{blue}{-28x} \color{blue}{+15} \\\Leftrightarrow & -24x-28x& = & 10+15 \\\Leftrightarrow & \color{red}{-52} x& = & 25 \\\Leftrightarrow & x = \frac{25}{-52} & & \\\Leftrightarrow & x = \frac{-25}{52} & & \\ & V = \left\{ \frac{-25}{52} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{4}{7})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -9x-\frac{12}{7}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x- \frac{60}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{-60} & = & \color{red}{-175x} +42 \\\Leftrightarrow & -315x \color{red}{-60} \color{blue}{+60} \color{blue}{+175x} & = & \color{red}{-175x} +42 \color{blue}{+175x} \color{blue}{+60} \\\Leftrightarrow & -315x+175x& = & 42+60 \\\Leftrightarrow & \color{red}{-140} x& = & 102 \\\Leftrightarrow & x = \frac{102}{-140} & & \\\Leftrightarrow & x = \frac{-51}{70} & & \\ & V = \left\{ \frac{-51}{70} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{3}{4})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -20x+\frac{15}{4}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-80}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{28}{ \color{blue}{4} }x+ \frac{6}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -80x \color{red}{+15} & = & \color{red}{28x} +6 \\\Leftrightarrow & -80x \color{red}{+15} \color{blue}{-15} \color{blue}{-28x} & = & \color{red}{28x} +6 \color{blue}{-28x} \color{blue}{-15} \\\Leftrightarrow & -80x-28x& = & 6-15 \\\Leftrightarrow & \color{red}{-108} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-108} & & \\\Leftrightarrow & x = \frac{1}{12} & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{5}{11})& = & -3x+\frac{9}{4} \\\Leftrightarrow & 16x+\frac{20}{11}& = & -3x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{704}{ \color{blue}{44} }x+ \frac{80}{ \color{blue}{44} })& = & (\frac{-132}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 704x \color{red}{+80} & = & \color{red}{-132x} +99 \\\Leftrightarrow & 704x \color{red}{+80} \color{blue}{-80} \color{blue}{+132x} & = & \color{red}{-132x} +99 \color{blue}{+132x} \color{blue}{-80} \\\Leftrightarrow & 704x+132x& = & 99-80 \\\Leftrightarrow & \color{red}{836} x& = & 19 \\\Leftrightarrow & x = \frac{19}{836} & & \\\Leftrightarrow & x = \frac{1}{44} & & \\ & V = \left\{ \frac{1}{44} \right\} & \\\end{align}\)