Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{5}{9})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 14x+\frac{35}{9}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{252}{ \color{blue}{18} }x+ \frac{70}{ \color{blue}{18} })& = & (\frac{90}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 252x \color{red}{+70} & = & \color{red}{90x} +81 \\\Leftrightarrow & 252x \color{red}{+70} \color{blue}{-70} \color{blue}{-90x} & = & \color{red}{90x} +81 \color{blue}{-90x} \color{blue}{-70} \\\Leftrightarrow & 252x-90x& = & 81-70 \\\Leftrightarrow & \color{red}{162} x& = & 11 \\\Leftrightarrow & x = \frac{11}{162} & & \\ & V = \left\{ \frac{11}{162} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{3}{5})& = & -2x+\frac{10}{9} \\\Leftrightarrow & 9x-\frac{9}{5}& = & -2x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{405}{ \color{blue}{45} }x- \frac{81}{ \color{blue}{45} })& = & (\frac{-90}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 405x \color{red}{-81} & = & \color{red}{-90x} +50 \\\Leftrightarrow & 405x \color{red}{-81} \color{blue}{+81} \color{blue}{+90x} & = & \color{red}{-90x} +50 \color{blue}{+90x} \color{blue}{+81} \\\Leftrightarrow & 405x+90x& = & 50+81 \\\Leftrightarrow & \color{red}{495} x& = & 131 \\\Leftrightarrow & x = \frac{131}{495} & & \\ & V = \left\{ \frac{131}{495} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{3}{11})& = & -5x+\frac{9}{10} \\\Leftrightarrow & 24x+\frac{18}{11}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{2640}{ \color{blue}{110} }x+ \frac{180}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 2640x \color{red}{+180} & = & \color{red}{-550x} +99 \\\Leftrightarrow & 2640x \color{red}{+180} \color{blue}{-180} \color{blue}{+550x} & = & \color{red}{-550x} +99 \color{blue}{+550x} \color{blue}{-180} \\\Leftrightarrow & 2640x+550x& = & 99-180 \\\Leftrightarrow & \color{red}{3190} x& = & -81 \\\Leftrightarrow & x = \frac{-81}{3190} & & \\ & V = \left\{ \frac{-81}{3190} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{4}{3})& = & -3x+\frac{4}{3} \\\Leftrightarrow & -8x-\frac{8}{3}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-24}{ \color{blue}{3} }x- \frac{8}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -24x \color{red}{-8} & = & \color{red}{-9x} +4 \\\Leftrightarrow & -24x \color{red}{-8} \color{blue}{+8} \color{blue}{+9x} & = & \color{red}{-9x} +4 \color{blue}{+9x} \color{blue}{+8} \\\Leftrightarrow & -24x+9x& = & 4+8 \\\Leftrightarrow & \color{red}{-15} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-15} & & \\\Leftrightarrow & x = \frac{-4}{5} & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{9})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -4x+\frac{8}{9}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-36}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -36x \color{red}{+8} & = & \color{red}{45x} +12 \\\Leftrightarrow & -36x \color{red}{+8} \color{blue}{-8} \color{blue}{-45x} & = & \color{red}{45x} +12 \color{blue}{-45x} \color{blue}{-8} \\\Leftrightarrow & -36x-45x& = & 12-8 \\\Leftrightarrow & \color{red}{-81} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-81} & & \\\Leftrightarrow & x = \frac{-4}{81} & & \\ & V = \left\{ \frac{-4}{81} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{1}{2})& = & 8x+\frac{2}{9} \\\Leftrightarrow & -15x-\frac{5}{2}& = & 8x+\frac{2}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-270}{ \color{blue}{18} }x- \frac{45}{ \color{blue}{18} })& = & (\frac{144}{ \color{blue}{18} }x+ \frac{4}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -270x \color{red}{-45} & = & \color{red}{144x} +4 \\\Leftrightarrow & -270x \color{red}{-45} \color{blue}{+45} \color{blue}{-144x} & = & \color{red}{144x} +4 \color{blue}{-144x} \color{blue}{+45} \\\Leftrightarrow & -270x-144x& = & 4+45 \\\Leftrightarrow & \color{red}{-414} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-414} & & \\\Leftrightarrow & x = \frac{-49}{414} & & \\ & V = \left\{ \frac{-49}{414} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{2}{11})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -16x+\frac{8}{11}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-176}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -176x \color{red}{+8} & = & \color{red}{77x} +6 \\\Leftrightarrow & -176x \color{red}{+8} \color{blue}{-8} \color{blue}{-77x} & = & \color{red}{77x} +6 \color{blue}{-77x} \color{blue}{-8} \\\Leftrightarrow & -176x-77x& = & 6-8 \\\Leftrightarrow & \color{red}{-253} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-253} & & \\\Leftrightarrow & x = \frac{2}{253} & & \\ & V = \left\{ \frac{2}{253} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{3}{8})& = & -2x+\frac{8}{11} \\\Leftrightarrow & 15x+\frac{15}{8}& = & -2x+\frac{8}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1320}{ \color{blue}{88} }x+ \frac{165}{ \color{blue}{88} })& = & (\frac{-176}{ \color{blue}{88} }x+ \frac{64}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1320x \color{red}{+165} & = & \color{red}{-176x} +64 \\\Leftrightarrow & 1320x \color{red}{+165} \color{blue}{-165} \color{blue}{+176x} & = & \color{red}{-176x} +64 \color{blue}{+176x} \color{blue}{-165} \\\Leftrightarrow & 1320x+176x& = & 64-165 \\\Leftrightarrow & \color{red}{1496} x& = & -101 \\\Leftrightarrow & x = \frac{-101}{1496} & & \\ & V = \left\{ \frac{-101}{1496} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{4}{3})& = & 5x+\frac{7}{8} \\\Leftrightarrow & 12x-\frac{16}{3}& = & 5x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{288}{ \color{blue}{24} }x- \frac{128}{ \color{blue}{24} })& = & (\frac{120}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 288x \color{red}{-128} & = & \color{red}{120x} +21 \\\Leftrightarrow & 288x \color{red}{-128} \color{blue}{+128} \color{blue}{-120x} & = & \color{red}{120x} +21 \color{blue}{-120x} \color{blue}{+128} \\\Leftrightarrow & 288x-120x& = & 21+128 \\\Leftrightarrow & \color{red}{168} x& = & 149 \\\Leftrightarrow & x = \frac{149}{168} & & \\ & V = \left\{ \frac{149}{168} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{5}{8})& = & 7x+\frac{9}{4} \\\Leftrightarrow & -6x+\frac{15}{8}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-48}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{56}{ \color{blue}{8} }x+ \frac{18}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -48x \color{red}{+15} & = & \color{red}{56x} +18 \\\Leftrightarrow & -48x \color{red}{+15} \color{blue}{-15} \color{blue}{-56x} & = & \color{red}{56x} +18 \color{blue}{-56x} \color{blue}{-15} \\\Leftrightarrow & -48x-56x& = & 18-15 \\\Leftrightarrow & \color{red}{-104} x& = & 3 \\\Leftrightarrow & x = \frac{3}{-104} & & \\\Leftrightarrow & x = \frac{-3}{104} & & \\ & V = \left\{ \frac{-3}{104} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{3}{7})& = & 3x+\frac{4}{9} \\\Leftrightarrow & 10x+\frac{6}{7}& = & 3x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{630}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 630x \color{red}{+54} & = & \color{red}{189x} +28 \\\Leftrightarrow & 630x \color{red}{+54} \color{blue}{-54} \color{blue}{-189x} & = & \color{red}{189x} +28 \color{blue}{-189x} \color{blue}{-54} \\\Leftrightarrow & 630x-189x& = & 28-54 \\\Leftrightarrow & \color{red}{441} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{441} & & \\ & V = \left\{ \frac{-26}{441} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{2}{9})& = & -7x+\frac{8}{9} \\\Leftrightarrow & -10x-\frac{4}{9}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x- \frac{4}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{-4} & = & \color{red}{-63x} +8 \\\Leftrightarrow & -90x \color{red}{-4} \color{blue}{+4} \color{blue}{+63x} & = & \color{red}{-63x} +8 \color{blue}{+63x} \color{blue}{+4} \\\Leftrightarrow & -90x+63x& = & 8+4 \\\Leftrightarrow & \color{red}{-27} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-27} & & \\\Leftrightarrow & x = \frac{-4}{9} & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)