Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{3}{11})& = & -7x+\frac{5}{6} \\\Leftrightarrow & -6x+\frac{6}{11}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-396}{ \color{blue}{66} }x+ \frac{36}{ \color{blue}{66} })& = & (\frac{-462}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -396x \color{red}{+36} & = & \color{red}{-462x} +55 \\\Leftrightarrow & -396x \color{red}{+36} \color{blue}{-36} \color{blue}{+462x} & = & \color{red}{-462x} +55 \color{blue}{+462x} \color{blue}{-36} \\\Leftrightarrow & -396x+462x& = & 55-36 \\\Leftrightarrow & \color{red}{66} x& = & 19 \\\Leftrightarrow & x = \frac{19}{66} & & \\ & V = \left\{ \frac{19}{66} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{3}{7})& = & -7x+\frac{8}{5} \\\Leftrightarrow & 4x-\frac{6}{7}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{-30} & = & \color{red}{-245x} +56 \\\Leftrightarrow & 140x \color{red}{-30} \color{blue}{+30} \color{blue}{+245x} & = & \color{red}{-245x} +56 \color{blue}{+245x} \color{blue}{+30} \\\Leftrightarrow & 140x+245x& = & 56+30 \\\Leftrightarrow & \color{red}{385} x& = & 86 \\\Leftrightarrow & x = \frac{86}{385} & & \\ & V = \left\{ \frac{86}{385} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{5}{11})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 18x-\frac{30}{11}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{396}{ \color{blue}{22} }x- \frac{60}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 396x \color{red}{-60} & = & \color{red}{110x} +99 \\\Leftrightarrow & 396x \color{red}{-60} \color{blue}{+60} \color{blue}{-110x} & = & \color{red}{110x} +99 \color{blue}{-110x} \color{blue}{+60} \\\Leftrightarrow & 396x-110x& = & 99+60 \\\Leftrightarrow & \color{red}{286} x& = & 159 \\\Leftrightarrow & x = \frac{159}{286} & & \\ & V = \left\{ \frac{159}{286} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{2}{3})& = & 2x+\frac{3}{2} \\\Leftrightarrow & 35x-\frac{14}{3}& = & 2x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{210}{ \color{blue}{6} }x- \frac{28}{ \color{blue}{6} })& = & (\frac{12}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 210x \color{red}{-28} & = & \color{red}{12x} +9 \\\Leftrightarrow & 210x \color{red}{-28} \color{blue}{+28} \color{blue}{-12x} & = & \color{red}{12x} +9 \color{blue}{-12x} \color{blue}{+28} \\\Leftrightarrow & 210x-12x& = & 9+28 \\\Leftrightarrow & \color{red}{198} x& = & 37 \\\Leftrightarrow & x = \frac{37}{198} & & \\ & V = \left\{ \frac{37}{198} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{3}{5})& = & -5x+\frac{3}{11} \\\Leftrightarrow & 12x-\frac{18}{5}& = & -5x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{198}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-198} & = & \color{red}{-275x} +15 \\\Leftrightarrow & 660x \color{red}{-198} \color{blue}{+198} \color{blue}{+275x} & = & \color{red}{-275x} +15 \color{blue}{+275x} \color{blue}{+198} \\\Leftrightarrow & 660x+275x& = & 15+198 \\\Leftrightarrow & \color{red}{935} x& = & 213 \\\Leftrightarrow & x = \frac{213}{935} & & \\ & V = \left\{ \frac{213}{935} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{2}{3})& = & -5x+\frac{9}{8} \\\Leftrightarrow & -12x+\frac{8}{3}& = & -5x+\frac{9}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-288}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} })& = & (\frac{-120}{ \color{blue}{24} }x+ \frac{27}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -288x \color{red}{+64} & = & \color{red}{-120x} +27 \\\Leftrightarrow & -288x \color{red}{+64} \color{blue}{-64} \color{blue}{+120x} & = & \color{red}{-120x} +27 \color{blue}{+120x} \color{blue}{-64} \\\Leftrightarrow & -288x+120x& = & 27-64 \\\Leftrightarrow & \color{red}{-168} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-168} & & \\\Leftrightarrow & x = \frac{37}{168} & & \\ & V = \left\{ \frac{37}{168} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{5}{7})& = & 3x+\frac{4}{5} \\\Leftrightarrow & 8x-\frac{20}{7}& = & 3x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{-100} & = & \color{red}{105x} +28 \\\Leftrightarrow & 280x \color{red}{-100} \color{blue}{+100} \color{blue}{-105x} & = & \color{red}{105x} +28 \color{blue}{-105x} \color{blue}{+100} \\\Leftrightarrow & 280x-105x& = & 28+100 \\\Leftrightarrow & \color{red}{175} x& = & 128 \\\Leftrightarrow & x = \frac{128}{175} & & \\ & V = \left\{ \frac{128}{175} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{3}{5})& = & -9x+\frac{3}{10} \\\Leftrightarrow & -8x-\frac{12}{5}& = & -9x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-80}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -80x \color{red}{-24} & = & \color{red}{-90x} +3 \\\Leftrightarrow & -80x \color{red}{-24} \color{blue}{+24} \color{blue}{+90x} & = & \color{red}{-90x} +3 \color{blue}{+90x} \color{blue}{+24} \\\Leftrightarrow & -80x+90x& = & 3+24 \\\Leftrightarrow & \color{red}{10} x& = & 27 \\\Leftrightarrow & x = \frac{27}{10} & & \\ & V = \left\{ \frac{27}{10} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{5}{3})& = & 9x+\frac{6}{11} \\\Leftrightarrow & -8x-\frac{20}{3}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{-220} & = & \color{red}{297x} +18 \\\Leftrightarrow & -264x \color{red}{-220} \color{blue}{+220} \color{blue}{-297x} & = & \color{red}{297x} +18 \color{blue}{-297x} \color{blue}{+220} \\\Leftrightarrow & -264x-297x& = & 18+220 \\\Leftrightarrow & \color{red}{-561} x& = & 238 \\\Leftrightarrow & x = \frac{238}{-561} & & \\\Leftrightarrow & x = \frac{-14}{33} & & \\ & V = \left\{ \frac{-14}{33} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{5}{11})& = & -9x+\frac{10}{7} \\\Leftrightarrow & -35x-\frac{35}{11}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2695}{ \color{blue}{77} }x- \frac{245}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2695x \color{red}{-245} & = & \color{red}{-693x} +110 \\\Leftrightarrow & -2695x \color{red}{-245} \color{blue}{+245} \color{blue}{+693x} & = & \color{red}{-693x} +110 \color{blue}{+693x} \color{blue}{+245} \\\Leftrightarrow & -2695x+693x& = & 110+245 \\\Leftrightarrow & \color{red}{-2002} x& = & 355 \\\Leftrightarrow & x = \frac{355}{-2002} & & \\\Leftrightarrow & x = \frac{-355}{2002} & & \\ & V = \left\{ \frac{-355}{2002} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{4}{3})& = & -2x+\frac{9}{5} \\\Leftrightarrow & 15x+\frac{20}{3}& = & -2x+\frac{9}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{225}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{-30}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 225x \color{red}{+100} & = & \color{red}{-30x} +27 \\\Leftrightarrow & 225x \color{red}{+100} \color{blue}{-100} \color{blue}{+30x} & = & \color{red}{-30x} +27 \color{blue}{+30x} \color{blue}{-100} \\\Leftrightarrow & 225x+30x& = & 27-100 \\\Leftrightarrow & \color{red}{255} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{255} & & \\ & V = \left\{ \frac{-73}{255} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{5}{7})& = & -9x+\frac{4}{3} \\\Leftrightarrow & -4x-\frac{10}{7}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-84}{ \color{blue}{21} }x- \frac{30}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -84x \color{red}{-30} & = & \color{red}{-189x} +28 \\\Leftrightarrow & -84x \color{red}{-30} \color{blue}{+30} \color{blue}{+189x} & = & \color{red}{-189x} +28 \color{blue}{+189x} \color{blue}{+30} \\\Leftrightarrow & -84x+189x& = & 28+30 \\\Leftrightarrow & \color{red}{105} x& = & 58 \\\Leftrightarrow & x = \frac{58}{105} & & \\ & V = \left\{ \frac{58}{105} \right\} & \\\end{align}\)