Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{3}{2})& = & -5x+\frac{9}{4} \\\Leftrightarrow & -12x+\frac{9}{2}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-48}{ \color{blue}{4} }x+ \frac{18}{ \color{blue}{4} })& = & (\frac{-20}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -48x \color{red}{+18} & = & \color{red}{-20x} +9 \\\Leftrightarrow & -48x \color{red}{+18} \color{blue}{-18} \color{blue}{+20x} & = & \color{red}{-20x} +9 \color{blue}{+20x} \color{blue}{-18} \\\Leftrightarrow & -48x+20x& = & 9-18 \\\Leftrightarrow & \color{red}{-28} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-28} & & \\\Leftrightarrow & x = \frac{9}{28} & & \\ & V = \left\{ \frac{9}{28} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{3}{11})& = & -5x+\frac{4}{5} \\\Leftrightarrow & 24x-\frac{18}{11}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x- \frac{90}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{-90} & = & \color{red}{-275x} +44 \\\Leftrightarrow & 1320x \color{red}{-90} \color{blue}{+90} \color{blue}{+275x} & = & \color{red}{-275x} +44 \color{blue}{+275x} \color{blue}{+90} \\\Leftrightarrow & 1320x+275x& = & 44+90 \\\Leftrightarrow & \color{red}{1595} x& = & 134 \\\Leftrightarrow & x = \frac{134}{1595} & & \\ & V = \left\{ \frac{134}{1595} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{5}{4})& = & 8x+\frac{8}{9} \\\Leftrightarrow & 15x-\frac{15}{4}& = & 8x+\frac{8}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{540}{ \color{blue}{36} }x- \frac{135}{ \color{blue}{36} })& = & (\frac{288}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 540x \color{red}{-135} & = & \color{red}{288x} +32 \\\Leftrightarrow & 540x \color{red}{-135} \color{blue}{+135} \color{blue}{-288x} & = & \color{red}{288x} +32 \color{blue}{-288x} \color{blue}{+135} \\\Leftrightarrow & 540x-288x& = & 32+135 \\\Leftrightarrow & \color{red}{252} x& = & 167 \\\Leftrightarrow & x = \frac{167}{252} & & \\ & V = \left\{ \frac{167}{252} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{3})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -4x+\frac{8}{3}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-60}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -60x \color{red}{+40} & = & \color{red}{-135x} +18 \\\Leftrightarrow & -60x \color{red}{+40} \color{blue}{-40} \color{blue}{+135x} & = & \color{red}{-135x} +18 \color{blue}{+135x} \color{blue}{-40} \\\Leftrightarrow & -60x+135x& = & 18-40 \\\Leftrightarrow & \color{red}{75} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{75} & & \\ & V = \left\{ \frac{-22}{75} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{2}{5})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -30x-\frac{12}{5}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{-84} & = & \color{red}{245x} +50 \\\Leftrightarrow & -1050x \color{red}{-84} \color{blue}{+84} \color{blue}{-245x} & = & \color{red}{245x} +50 \color{blue}{-245x} \color{blue}{+84} \\\Leftrightarrow & -1050x-245x& = & 50+84 \\\Leftrightarrow & \color{red}{-1295} x& = & 134 \\\Leftrightarrow & x = \frac{134}{-1295} & & \\\Leftrightarrow & x = \frac{-134}{1295} & & \\ & V = \left\{ \frac{-134}{1295} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{5}{7})& = & 3x+\frac{10}{9} \\\Leftrightarrow & 4x-\frac{10}{7}& = & 3x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{252}{ \color{blue}{63} }x- \frac{90}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 252x \color{red}{-90} & = & \color{red}{189x} +70 \\\Leftrightarrow & 252x \color{red}{-90} \color{blue}{+90} \color{blue}{-189x} & = & \color{red}{189x} +70 \color{blue}{-189x} \color{blue}{+90} \\\Leftrightarrow & 252x-189x& = & 70+90 \\\Leftrightarrow & \color{red}{63} x& = & 160 \\\Leftrightarrow & x = \frac{160}{63} & & \\ & V = \left\{ \frac{160}{63} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{2}{9})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -8x-\frac{4}{9}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-360}{ \color{blue}{45} }x- \frac{20}{ \color{blue}{45} })& = & (\frac{-405}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -360x \color{red}{-20} & = & \color{red}{-405x} +54 \\\Leftrightarrow & -360x \color{red}{-20} \color{blue}{+20} \color{blue}{+405x} & = & \color{red}{-405x} +54 \color{blue}{+405x} \color{blue}{+20} \\\Leftrightarrow & -360x+405x& = & 54+20 \\\Leftrightarrow & \color{red}{45} x& = & 74 \\\Leftrightarrow & x = \frac{74}{45} & & \\ & V = \left\{ \frac{74}{45} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{3}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 6x+\frac{6}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{+30} & = & \color{red}{-245x} +42 \\\Leftrightarrow & 210x \color{red}{+30} \color{blue}{-30} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{-30} \\\Leftrightarrow & 210x+245x& = & 42-30 \\\Leftrightarrow & \color{red}{455} x& = & 12 \\\Leftrightarrow & x = \frac{12}{455} & & \\ & V = \left\{ \frac{12}{455} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{5}{8})& = & 8x+\frac{7}{10} \\\Leftrightarrow & -15x+\frac{15}{8}& = & 8x+\frac{7}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-600}{ \color{blue}{40} }x+ \frac{75}{ \color{blue}{40} })& = & (\frac{320}{ \color{blue}{40} }x+ \frac{28}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -600x \color{red}{+75} & = & \color{red}{320x} +28 \\\Leftrightarrow & -600x \color{red}{+75} \color{blue}{-75} \color{blue}{-320x} & = & \color{red}{320x} +28 \color{blue}{-320x} \color{blue}{-75} \\\Leftrightarrow & -600x-320x& = & 28-75 \\\Leftrightarrow & \color{red}{-920} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{-920} & & \\\Leftrightarrow & x = \frac{47}{920} & & \\ & V = \left\{ \frac{47}{920} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{5}{11})& = & -9x+\frac{4}{3} \\\Leftrightarrow & -4x-\frac{10}{11}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-132}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -132x \color{red}{-30} & = & \color{red}{-297x} +44 \\\Leftrightarrow & -132x \color{red}{-30} \color{blue}{+30} \color{blue}{+297x} & = & \color{red}{-297x} +44 \color{blue}{+297x} \color{blue}{+30} \\\Leftrightarrow & -132x+297x& = & 44+30 \\\Leftrightarrow & \color{red}{165} x& = & 74 \\\Leftrightarrow & x = \frac{74}{165} & & \\ & V = \left\{ \frac{74}{165} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{2}{5})& = & 5x+\frac{5}{11} \\\Leftrightarrow & 6x-\frac{4}{5}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x- \frac{44}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{-44} & = & \color{red}{275x} +25 \\\Leftrightarrow & 330x \color{red}{-44} \color{blue}{+44} \color{blue}{-275x} & = & \color{red}{275x} +25 \color{blue}{-275x} \color{blue}{+44} \\\Leftrightarrow & 330x-275x& = & 25+44 \\\Leftrightarrow & \color{red}{55} x& = & 69 \\\Leftrightarrow & x = \frac{69}{55} & & \\ & V = \left\{ \frac{69}{55} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{4}{5})& = & -5x+\frac{8}{3} \\\Leftrightarrow & -9x-\frac{12}{5}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-135}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -135x \color{red}{-36} & = & \color{red}{-75x} +40 \\\Leftrightarrow & -135x \color{red}{-36} \color{blue}{+36} \color{blue}{+75x} & = & \color{red}{-75x} +40 \color{blue}{+75x} \color{blue}{+36} \\\Leftrightarrow & -135x+75x& = & 40+36 \\\Leftrightarrow & \color{red}{-60} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-60} & & \\\Leftrightarrow & x = \frac{-19}{15} & & \\ & V = \left\{ \frac{-19}{15} \right\} & \\\end{align}\)