Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{5}{11})& = & -2x+\frac{6}{5} \\\Leftrightarrow & 15x-\frac{25}{11}& = & -2x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x- \frac{125}{ \color{blue}{55} })& = & (\frac{-110}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{-125} & = & \color{red}{-110x} +66 \\\Leftrightarrow & 825x \color{red}{-125} \color{blue}{+125} \color{blue}{+110x} & = & \color{red}{-110x} +66 \color{blue}{+110x} \color{blue}{+125} \\\Leftrightarrow & 825x+110x& = & 66+125 \\\Leftrightarrow & \color{red}{935} x& = & 191 \\\Leftrightarrow & x = \frac{191}{935} & & \\ & V = \left\{ \frac{191}{935} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{2}{3})& = & 3x+\frac{9}{4} \\\Leftrightarrow & -35x-\frac{14}{3}& = & 3x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-420}{ \color{blue}{12} }x- \frac{56}{ \color{blue}{12} })& = & (\frac{36}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -420x \color{red}{-56} & = & \color{red}{36x} +27 \\\Leftrightarrow & -420x \color{red}{-56} \color{blue}{+56} \color{blue}{-36x} & = & \color{red}{36x} +27 \color{blue}{-36x} \color{blue}{+56} \\\Leftrightarrow & -420x-36x& = & 27+56 \\\Leftrightarrow & \color{red}{-456} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-456} & & \\\Leftrightarrow & x = \frac{-83}{456} & & \\ & V = \left\{ \frac{-83}{456} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{5}{3})& = & 8x+\frac{3}{4} \\\Leftrightarrow & 35x+\frac{35}{3}& = & 8x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{420}{ \color{blue}{12} }x+ \frac{140}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 420x \color{red}{+140} & = & \color{red}{96x} +9 \\\Leftrightarrow & 420x \color{red}{+140} \color{blue}{-140} \color{blue}{-96x} & = & \color{red}{96x} +9 \color{blue}{-96x} \color{blue}{-140} \\\Leftrightarrow & 420x-96x& = & 9-140 \\\Leftrightarrow & \color{red}{324} x& = & -131 \\\Leftrightarrow & x = \frac{-131}{324} & & \\ & V = \left\{ \frac{-131}{324} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{3}{7})& = & 7x+\frac{2}{11} \\\Leftrightarrow & -6x-\frac{6}{7}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{-66} & = & \color{red}{539x} +14 \\\Leftrightarrow & -462x \color{red}{-66} \color{blue}{+66} \color{blue}{-539x} & = & \color{red}{539x} +14 \color{blue}{-539x} \color{blue}{+66} \\\Leftrightarrow & -462x-539x& = & 14+66 \\\Leftrightarrow & \color{red}{-1001} x& = & 80 \\\Leftrightarrow & x = \frac{80}{-1001} & & \\\Leftrightarrow & x = \frac{-80}{1001} & & \\ & V = \left\{ \frac{-80}{1001} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{5}{8})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 12x-\frac{15}{8}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{288}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 288x \color{red}{-45} & = & \color{red}{168x} +80 \\\Leftrightarrow & 288x \color{red}{-45} \color{blue}{+45} \color{blue}{-168x} & = & \color{red}{168x} +80 \color{blue}{-168x} \color{blue}{+45} \\\Leftrightarrow & 288x-168x& = & 80+45 \\\Leftrightarrow & \color{red}{120} x& = & 125 \\\Leftrightarrow & x = \frac{125}{120} & & \\\Leftrightarrow & x = \frac{25}{24} & & \\ & V = \left\{ \frac{25}{24} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{2}{11})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 24x+\frac{12}{11}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{264}{ \color{blue}{11} }x+ \frac{12}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 264x \color{red}{+12} & = & \color{red}{-55x} +6 \\\Leftrightarrow & 264x \color{red}{+12} \color{blue}{-12} \color{blue}{+55x} & = & \color{red}{-55x} +6 \color{blue}{+55x} \color{blue}{-12} \\\Leftrightarrow & 264x+55x& = & 6-12 \\\Leftrightarrow & \color{red}{319} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{319} & & \\ & V = \left\{ \frac{-6}{319} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{5}{2})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -6x-\frac{15}{2}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-36}{ \color{blue}{6} }x- \frac{45}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -36x \color{red}{-45} & = & \color{red}{42x} +16 \\\Leftrightarrow & -36x \color{red}{-45} \color{blue}{+45} \color{blue}{-42x} & = & \color{red}{42x} +16 \color{blue}{-42x} \color{blue}{+45} \\\Leftrightarrow & -36x-42x& = & 16+45 \\\Leftrightarrow & \color{red}{-78} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-78} & & \\\Leftrightarrow & x = \frac{-61}{78} & & \\ & V = \left\{ \frac{-61}{78} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{5}{8})& = & -2x+\frac{9}{4} \\\Leftrightarrow & 9x+\frac{15}{8}& = & -2x+\frac{9}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{72}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{-16}{ \color{blue}{8} }x+ \frac{18}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 72x \color{red}{+15} & = & \color{red}{-16x} +18 \\\Leftrightarrow & 72x \color{red}{+15} \color{blue}{-15} \color{blue}{+16x} & = & \color{red}{-16x} +18 \color{blue}{+16x} \color{blue}{-15} \\\Leftrightarrow & 72x+16x& = & 18-15 \\\Leftrightarrow & \color{red}{88} x& = & 3 \\\Leftrightarrow & x = \frac{3}{88} & & \\ & V = \left\{ \frac{3}{88} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{7})& = & 5x+\frac{5}{2} \\\Leftrightarrow & -4x+\frac{4}{7}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-56}{ \color{blue}{14} }x+ \frac{8}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -56x \color{red}{+8} & = & \color{red}{70x} +35 \\\Leftrightarrow & -56x \color{red}{+8} \color{blue}{-8} \color{blue}{-70x} & = & \color{red}{70x} +35 \color{blue}{-70x} \color{blue}{-8} \\\Leftrightarrow & -56x-70x& = & 35-8 \\\Leftrightarrow & \color{red}{-126} x& = & 27 \\\Leftrightarrow & x = \frac{27}{-126} & & \\\Leftrightarrow & x = \frac{-3}{14} & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{2}{9})& = & 8x+\frac{4}{9} \\\Leftrightarrow & -21x+\frac{14}{9}& = & 8x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-189}{ \color{blue}{9} }x+ \frac{14}{ \color{blue}{9} })& = & (\frac{72}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -189x \color{red}{+14} & = & \color{red}{72x} +4 \\\Leftrightarrow & -189x \color{red}{+14} \color{blue}{-14} \color{blue}{-72x} & = & \color{red}{72x} +4 \color{blue}{-72x} \color{blue}{-14} \\\Leftrightarrow & -189x-72x& = & 4-14 \\\Leftrightarrow & \color{red}{-261} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-261} & & \\\Leftrightarrow & x = \frac{10}{261} & & \\ & V = \left\{ \frac{10}{261} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{2}{5})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -6x+\frac{4}{5}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-270}{ \color{blue}{45} }x+ \frac{36}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -270x \color{red}{+36} & = & \color{red}{-315x} +20 \\\Leftrightarrow & -270x \color{red}{+36} \color{blue}{-36} \color{blue}{+315x} & = & \color{red}{-315x} +20 \color{blue}{+315x} \color{blue}{-36} \\\Leftrightarrow & -270x+315x& = & 20-36 \\\Leftrightarrow & \color{red}{45} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{45} & & \\ & V = \left\{ \frac{-16}{45} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{4}{9})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -16x-\frac{16}{9}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-720}{ \color{blue}{45} }x- \frac{80}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -720x \color{red}{-80} & = & \color{red}{315x} +54 \\\Leftrightarrow & -720x \color{red}{-80} \color{blue}{+80} \color{blue}{-315x} & = & \color{red}{315x} +54 \color{blue}{-315x} \color{blue}{+80} \\\Leftrightarrow & -720x-315x& = & 54+80 \\\Leftrightarrow & \color{red}{-1035} x& = & 134 \\\Leftrightarrow & x = \frac{134}{-1035} & & \\\Leftrightarrow & x = \frac{-134}{1035} & & \\ & V = \left\{ \frac{-134}{1035} \right\} & \\\end{align}\)