Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{2}{5})& = & -5x+\frac{7}{12} \\\Leftrightarrow & 6x-\frac{6}{5}& = & -5x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{360}{ \color{blue}{60} }x- \frac{72}{ \color{blue}{60} })& = & (\frac{-300}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 360x \color{red}{-72} & = & \color{red}{-300x} +35 \\\Leftrightarrow & 360x \color{red}{-72} \color{blue}{+72} \color{blue}{+300x} & = & \color{red}{-300x} +35 \color{blue}{+300x} \color{blue}{+72} \\\Leftrightarrow & 360x+300x& = & 35+72 \\\Leftrightarrow & \color{red}{660} x& = & 107 \\\Leftrightarrow & x = \frac{107}{660} & & \\ & V = \left\{ \frac{107}{660} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{3}{5})& = & 9x+\frac{10}{11} \\\Leftrightarrow & -4x+\frac{6}{5}& = & 9x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-220}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -220x \color{red}{+66} & = & \color{red}{495x} +50 \\\Leftrightarrow & -220x \color{red}{+66} \color{blue}{-66} \color{blue}{-495x} & = & \color{red}{495x} +50 \color{blue}{-495x} \color{blue}{-66} \\\Leftrightarrow & -220x-495x& = & 50-66 \\\Leftrightarrow & \color{red}{-715} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-715} & & \\\Leftrightarrow & x = \frac{16}{715} & & \\ & V = \left\{ \frac{16}{715} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{2}{7})& = & 7x+\frac{5}{6} \\\Leftrightarrow & 10x+\frac{10}{7}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{420}{ \color{blue}{42} }x+ \frac{60}{ \color{blue}{42} })& = & (\frac{294}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 420x \color{red}{+60} & = & \color{red}{294x} +35 \\\Leftrightarrow & 420x \color{red}{+60} \color{blue}{-60} \color{blue}{-294x} & = & \color{red}{294x} +35 \color{blue}{-294x} \color{blue}{-60} \\\Leftrightarrow & 420x-294x& = & 35-60 \\\Leftrightarrow & \color{red}{126} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{126} & & \\ & V = \left\{ \frac{-25}{126} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{4}{9})& = & 8x+\frac{10}{9} \\\Leftrightarrow & -28x-\frac{28}{9}& = & 8x+\frac{10}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-252}{ \color{blue}{9} }x- \frac{28}{ \color{blue}{9} })& = & (\frac{72}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -252x \color{red}{-28} & = & \color{red}{72x} +10 \\\Leftrightarrow & -252x \color{red}{-28} \color{blue}{+28} \color{blue}{-72x} & = & \color{red}{72x} +10 \color{blue}{-72x} \color{blue}{+28} \\\Leftrightarrow & -252x-72x& = & 10+28 \\\Leftrightarrow & \color{red}{-324} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-324} & & \\\Leftrightarrow & x = \frac{-19}{162} & & \\ & V = \left\{ \frac{-19}{162} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{5}{9})& = & -7x+\frac{7}{4} \\\Leftrightarrow & -16x-\frac{20}{9}& = & -7x+\frac{7}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-576}{ \color{blue}{36} }x- \frac{80}{ \color{blue}{36} })& = & (\frac{-252}{ \color{blue}{36} }x+ \frac{63}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -576x \color{red}{-80} & = & \color{red}{-252x} +63 \\\Leftrightarrow & -576x \color{red}{-80} \color{blue}{+80} \color{blue}{+252x} & = & \color{red}{-252x} +63 \color{blue}{+252x} \color{blue}{+80} \\\Leftrightarrow & -576x+252x& = & 63+80 \\\Leftrightarrow & \color{red}{-324} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-324} & & \\\Leftrightarrow & x = \frac{-143}{324} & & \\ & V = \left\{ \frac{-143}{324} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{4}{3})& = & -3x+\frac{5}{9} \\\Leftrightarrow & -20x-\frac{20}{3}& = & -3x+\frac{5}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-180}{ \color{blue}{9} }x- \frac{60}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{5}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -180x \color{red}{-60} & = & \color{red}{-27x} +5 \\\Leftrightarrow & -180x \color{red}{-60} \color{blue}{+60} \color{blue}{+27x} & = & \color{red}{-27x} +5 \color{blue}{+27x} \color{blue}{+60} \\\Leftrightarrow & -180x+27x& = & 5+60 \\\Leftrightarrow & \color{red}{-153} x& = & 65 \\\Leftrightarrow & x = \frac{65}{-153} & & \\\Leftrightarrow & x = \frac{-65}{153} & & \\ & V = \left\{ \frac{-65}{153} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{2}{7})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 30x-\frac{12}{7}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{210}{ \color{blue}{7} }x- \frac{12}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 210x \color{red}{-12} & = & \color{red}{49x} +10 \\\Leftrightarrow & 210x \color{red}{-12} \color{blue}{+12} \color{blue}{-49x} & = & \color{red}{49x} +10 \color{blue}{-49x} \color{blue}{+12} \\\Leftrightarrow & 210x-49x& = & 10+12 \\\Leftrightarrow & \color{red}{161} x& = & 22 \\\Leftrightarrow & x = \frac{22}{161} & & \\ & V = \left\{ \frac{22}{161} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{3}{7})& = & 5x+\frac{2}{11} \\\Leftrightarrow & -4x+\frac{6}{7}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-308}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -308x \color{red}{+66} & = & \color{red}{385x} +14 \\\Leftrightarrow & -308x \color{red}{+66} \color{blue}{-66} \color{blue}{-385x} & = & \color{red}{385x} +14 \color{blue}{-385x} \color{blue}{-66} \\\Leftrightarrow & -308x-385x& = & 14-66 \\\Leftrightarrow & \color{red}{-693} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{-693} & & \\\Leftrightarrow & x = \frac{52}{693} & & \\ & V = \left\{ \frac{52}{693} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{5}{7})& = & -3x+\frac{7}{5} \\\Leftrightarrow & 8x+\frac{10}{7}& = & -3x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{49}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{+50} & = & \color{red}{-105x} +49 \\\Leftrightarrow & 280x \color{red}{+50} \color{blue}{-50} \color{blue}{+105x} & = & \color{red}{-105x} +49 \color{blue}{+105x} \color{blue}{-50} \\\Leftrightarrow & 280x+105x& = & 49-50 \\\Leftrightarrow & \color{red}{385} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{385} & & \\ & V = \left\{ \frac{-1}{385} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{2}{11})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 12x-\frac{12}{11}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{264}{ \color{blue}{22} }x- \frac{24}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 264x \color{red}{-24} & = & \color{red}{-110x} +99 \\\Leftrightarrow & 264x \color{red}{-24} \color{blue}{+24} \color{blue}{+110x} & = & \color{red}{-110x} +99 \color{blue}{+110x} \color{blue}{+24} \\\Leftrightarrow & 264x+110x& = & 99+24 \\\Leftrightarrow & \color{red}{374} x& = & 123 \\\Leftrightarrow & x = \frac{123}{374} & & \\ & V = \left\{ \frac{123}{374} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{7})& = & -7x+\frac{9}{7} \\\Leftrightarrow & -10x-\frac{15}{7}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x- \frac{15}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{-15} & = & \color{red}{-49x} +9 \\\Leftrightarrow & -70x \color{red}{-15} \color{blue}{+15} \color{blue}{+49x} & = & \color{red}{-49x} +9 \color{blue}{+49x} \color{blue}{+15} \\\Leftrightarrow & -70x+49x& = & 9+15 \\\Leftrightarrow & \color{red}{-21} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-21} & & \\\Leftrightarrow & x = \frac{-8}{7} & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{4}{3})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 6x-\frac{8}{3}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{90}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 90x \color{red}{-40} & = & \color{red}{-75x} +18 \\\Leftrightarrow & 90x \color{red}{-40} \color{blue}{+40} \color{blue}{+75x} & = & \color{red}{-75x} +18 \color{blue}{+75x} \color{blue}{+40} \\\Leftrightarrow & 90x+75x& = & 18+40 \\\Leftrightarrow & \color{red}{165} x& = & 58 \\\Leftrightarrow & x = \frac{58}{165} & & \\ & V = \left\{ \frac{58}{165} \right\} & \\\end{align}\)