Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{4}{5})& = & 7x+\frac{3}{8} \\\Leftrightarrow & 24x+\frac{24}{5}& = & 7x+\frac{3}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{960}{ \color{blue}{40} }x+ \frac{192}{ \color{blue}{40} })& = & (\frac{280}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 960x \color{red}{+192} & = & \color{red}{280x} +15 \\\Leftrightarrow & 960x \color{red}{+192} \color{blue}{-192} \color{blue}{-280x} & = & \color{red}{280x} +15 \color{blue}{-280x} \color{blue}{-192} \\\Leftrightarrow & 960x-280x& = & 15-192 \\\Leftrightarrow & \color{red}{680} x& = & -177 \\\Leftrightarrow & x = \frac{-177}{680} & & \\ & V = \left\{ \frac{-177}{680} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{4}{11})& = & -7x+\frac{9}{7} \\\Leftrightarrow & 4x+\frac{8}{11}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{308}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 308x \color{red}{+56} & = & \color{red}{-539x} +99 \\\Leftrightarrow & 308x \color{red}{+56} \color{blue}{-56} \color{blue}{+539x} & = & \color{red}{-539x} +99 \color{blue}{+539x} \color{blue}{-56} \\\Leftrightarrow & 308x+539x& = & 99-56 \\\Leftrightarrow & \color{red}{847} x& = & 43 \\\Leftrightarrow & x = \frac{43}{847} & & \\ & V = \left\{ \frac{43}{847} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{4}{9})& = & 3x+\frac{2}{11} \\\Leftrightarrow & 4x-\frac{8}{9}& = & 3x+\frac{2}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{396}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{18}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 396x \color{red}{-88} & = & \color{red}{297x} +18 \\\Leftrightarrow & 396x \color{red}{-88} \color{blue}{+88} \color{blue}{-297x} & = & \color{red}{297x} +18 \color{blue}{-297x} \color{blue}{+88} \\\Leftrightarrow & 396x-297x& = & 18+88 \\\Leftrightarrow & \color{red}{99} x& = & 106 \\\Leftrightarrow & x = \frac{106}{99} & & \\ & V = \left\{ \frac{106}{99} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{3}{2})& = & -2x+\frac{4}{5} \\\Leftrightarrow & 21x+\frac{21}{2}& = & -2x+\frac{4}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{210}{ \color{blue}{10} }x+ \frac{105}{ \color{blue}{10} })& = & (\frac{-20}{ \color{blue}{10} }x+ \frac{8}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 210x \color{red}{+105} & = & \color{red}{-20x} +8 \\\Leftrightarrow & 210x \color{red}{+105} \color{blue}{-105} \color{blue}{+20x} & = & \color{red}{-20x} +8 \color{blue}{+20x} \color{blue}{-105} \\\Leftrightarrow & 210x+20x& = & 8-105 \\\Leftrightarrow & \color{red}{230} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{230} & & \\ & V = \left\{ \frac{-97}{230} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{5}{11})& = & 5x+\frac{3}{7} \\\Leftrightarrow & -14x-\frac{35}{11}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1078}{ \color{blue}{77} }x- \frac{245}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1078x \color{red}{-245} & = & \color{red}{385x} +33 \\\Leftrightarrow & -1078x \color{red}{-245} \color{blue}{+245} \color{blue}{-385x} & = & \color{red}{385x} +33 \color{blue}{-385x} \color{blue}{+245} \\\Leftrightarrow & -1078x-385x& = & 33+245 \\\Leftrightarrow & \color{red}{-1463} x& = & 278 \\\Leftrightarrow & x = \frac{278}{-1463} & & \\\Leftrightarrow & x = \frac{-278}{1463} & & \\ & V = \left\{ \frac{-278}{1463} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{5}{12})& = & -9x+\frac{8}{7} \\\Leftrightarrow & 10x+\frac{25}{12}& = & -9x+\frac{8}{7} \\ & & & \text{kgv van noemers 12 en 7 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{840}{ \color{blue}{84} }x+ \frac{175}{ \color{blue}{84} })& = & (\frac{-756}{ \color{blue}{84} }x+ \frac{96}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 840x \color{red}{+175} & = & \color{red}{-756x} +96 \\\Leftrightarrow & 840x \color{red}{+175} \color{blue}{-175} \color{blue}{+756x} & = & \color{red}{-756x} +96 \color{blue}{+756x} \color{blue}{-175} \\\Leftrightarrow & 840x+756x& = & 96-175 \\\Leftrightarrow & \color{red}{1596} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{1596} & & \\ & V = \left\{ \frac{-79}{1596} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{2}{5})& = & 3x+\frac{5}{3} \\\Leftrightarrow & -18x+\frac{12}{5}& = & 3x+\frac{5}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-270}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{25}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -270x \color{red}{+36} & = & \color{red}{45x} +25 \\\Leftrightarrow & -270x \color{red}{+36} \color{blue}{-36} \color{blue}{-45x} & = & \color{red}{45x} +25 \color{blue}{-45x} \color{blue}{-36} \\\Leftrightarrow & -270x-45x& = & 25-36 \\\Leftrightarrow & \color{red}{-315} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-315} & & \\\Leftrightarrow & x = \frac{11}{315} & & \\ & V = \left\{ \frac{11}{315} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{3}{5})& = & 3x+\frac{4}{7} \\\Leftrightarrow & 4x-\frac{6}{5}& = & 3x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x- \frac{42}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{-42} & = & \color{red}{105x} +20 \\\Leftrightarrow & 140x \color{red}{-42} \color{blue}{+42} \color{blue}{-105x} & = & \color{red}{105x} +20 \color{blue}{-105x} \color{blue}{+42} \\\Leftrightarrow & 140x-105x& = & 20+42 \\\Leftrightarrow & \color{red}{35} x& = & 62 \\\Leftrightarrow & x = \frac{62}{35} & & \\ & V = \left\{ \frac{62}{35} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{2}{11})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -10x+\frac{4}{11}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-110}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -110x \color{red}{+4} & = & \color{red}{77x} +6 \\\Leftrightarrow & -110x \color{red}{+4} \color{blue}{-4} \color{blue}{-77x} & = & \color{red}{77x} +6 \color{blue}{-77x} \color{blue}{-4} \\\Leftrightarrow & -110x-77x& = & 6-4 \\\Leftrightarrow & \color{red}{-187} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-187} & & \\\Leftrightarrow & x = \frac{-2}{187} & & \\ & V = \left\{ \frac{-2}{187} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{2}{5})& = & -5x+\frac{2}{11} \\\Leftrightarrow & 4x-\frac{4}{5}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{220}{ \color{blue}{55} }x- \frac{44}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 220x \color{red}{-44} & = & \color{red}{-275x} +10 \\\Leftrightarrow & 220x \color{red}{-44} \color{blue}{+44} \color{blue}{+275x} & = & \color{red}{-275x} +10 \color{blue}{+275x} \color{blue}{+44} \\\Leftrightarrow & 220x+275x& = & 10+44 \\\Leftrightarrow & \color{red}{495} x& = & 54 \\\Leftrightarrow & x = \frac{54}{495} & & \\\Leftrightarrow & x = \frac{6}{55} & & \\ & V = \left\{ \frac{6}{55} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{4}{5})& = & 5x+\frac{8}{7} \\\Leftrightarrow & 18x+\frac{24}{5}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x+ \frac{168}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{+168} & = & \color{red}{175x} +40 \\\Leftrightarrow & 630x \color{red}{+168} \color{blue}{-168} \color{blue}{-175x} & = & \color{red}{175x} +40 \color{blue}{-175x} \color{blue}{-168} \\\Leftrightarrow & 630x-175x& = & 40-168 \\\Leftrightarrow & \color{red}{455} x& = & -128 \\\Leftrightarrow & x = \frac{-128}{455} & & \\ & V = \left\{ \frac{-128}{455} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{4}{5})& = & -7x+\frac{6}{7} \\\Leftrightarrow & -30x+\frac{24}{5}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x+ \frac{168}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{+168} & = & \color{red}{-245x} +30 \\\Leftrightarrow & -1050x \color{red}{+168} \color{blue}{-168} \color{blue}{+245x} & = & \color{red}{-245x} +30 \color{blue}{+245x} \color{blue}{-168} \\\Leftrightarrow & -1050x+245x& = & 30-168 \\\Leftrightarrow & \color{red}{-805} x& = & -138 \\\Leftrightarrow & x = \frac{-138}{-805} & & \\\Leftrightarrow & x = \frac{6}{35} & & \\ & V = \left\{ \frac{6}{35} \right\} & \\\end{align}\)