Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-2)& = & 6x+\frac{8}{3} \\\Leftrightarrow & 35x+14& = & 6x+\frac{8}{3} \\ & & & \text{kgv van noemers 1 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{105}{ \color{blue}{3} }x+ \frac{42}{ \color{blue}{3} })& = & (\frac{18}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 105x \color{red}{+42} & = & \color{red}{18x} +8 \\\Leftrightarrow & 105x \color{red}{+42} \color{blue}{-42} \color{blue}{-18x} & = & \color{red}{18x} +8 \color{blue}{-18x} \color{blue}{-42} \\\Leftrightarrow & 105x-18x& = & 8-42 \\\Leftrightarrow & \color{red}{87} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{87} & & \\ & V = \left\{ \frac{-34}{87} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{4}{5})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -30x+\frac{24}{5}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{+264} & = & \color{red}{-385x} +30 \\\Leftrightarrow & -1650x \color{red}{+264} \color{blue}{-264} \color{blue}{+385x} & = & \color{red}{-385x} +30 \color{blue}{+385x} \color{blue}{-264} \\\Leftrightarrow & -1650x+385x& = & 30-264 \\\Leftrightarrow & \color{red}{-1265} x& = & -234 \\\Leftrightarrow & x = \frac{-234}{-1265} & & \\\Leftrightarrow & x = \frac{234}{1265} & & \\ & V = \left\{ \frac{234}{1265} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{4}{5})& = & 4x+\frac{7}{8} \\\Leftrightarrow & -18x-\frac{24}{5}& = & 4x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-720}{ \color{blue}{40} }x- \frac{192}{ \color{blue}{40} })& = & (\frac{160}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -720x \color{red}{-192} & = & \color{red}{160x} +35 \\\Leftrightarrow & -720x \color{red}{-192} \color{blue}{+192} \color{blue}{-160x} & = & \color{red}{160x} +35 \color{blue}{-160x} \color{blue}{+192} \\\Leftrightarrow & -720x-160x& = & 35+192 \\\Leftrightarrow & \color{red}{-880} x& = & 227 \\\Leftrightarrow & x = \frac{227}{-880} & & \\\Leftrightarrow & x = \frac{-227}{880} & & \\ & V = \left\{ \frac{-227}{880} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{5}{12})& = & 3x+\frac{2}{3} \\\Leftrightarrow & -14x-\frac{35}{12}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 12 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-168}{ \color{blue}{12} }x- \frac{35}{ \color{blue}{12} })& = & (\frac{36}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -168x \color{red}{-35} & = & \color{red}{36x} +8 \\\Leftrightarrow & -168x \color{red}{-35} \color{blue}{+35} \color{blue}{-36x} & = & \color{red}{36x} +8 \color{blue}{-36x} \color{blue}{+35} \\\Leftrightarrow & -168x-36x& = & 8+35 \\\Leftrightarrow & \color{red}{-204} x& = & 43 \\\Leftrightarrow & x = \frac{43}{-204} & & \\\Leftrightarrow & x = \frac{-43}{204} & & \\ & V = \left\{ \frac{-43}{204} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{2}{3})& = & -7x+\frac{7}{2} \\\Leftrightarrow & 8x+\frac{4}{3}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{48}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 48x \color{red}{+8} & = & \color{red}{-42x} +21 \\\Leftrightarrow & 48x \color{red}{+8} \color{blue}{-8} \color{blue}{+42x} & = & \color{red}{-42x} +21 \color{blue}{+42x} \color{blue}{-8} \\\Leftrightarrow & 48x+42x& = & 21-8 \\\Leftrightarrow & \color{red}{90} x& = & 13 \\\Leftrightarrow & x = \frac{13}{90} & & \\ & V = \left\{ \frac{13}{90} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{2}{3})& = & 3x+\frac{7}{12} \\\Leftrightarrow & -35x+\frac{14}{3}& = & 3x+\frac{7}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-420}{ \color{blue}{12} }x+ \frac{56}{ \color{blue}{12} })& = & (\frac{36}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -420x \color{red}{+56} & = & \color{red}{36x} +7 \\\Leftrightarrow & -420x \color{red}{+56} \color{blue}{-56} \color{blue}{-36x} & = & \color{red}{36x} +7 \color{blue}{-36x} \color{blue}{-56} \\\Leftrightarrow & -420x-36x& = & 7-56 \\\Leftrightarrow & \color{red}{-456} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{-456} & & \\\Leftrightarrow & x = \frac{49}{456} & & \\ & V = \left\{ \frac{49}{456} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{2}{3})& = & -9x+\frac{9}{5} \\\Leftrightarrow & -20x-\frac{8}{3}& = & -9x+\frac{9}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{-40} & = & \color{red}{-135x} +27 \\\Leftrightarrow & -300x \color{red}{-40} \color{blue}{+40} \color{blue}{+135x} & = & \color{red}{-135x} +27 \color{blue}{+135x} \color{blue}{+40} \\\Leftrightarrow & -300x+135x& = & 27+40 \\\Leftrightarrow & \color{red}{-165} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-165} & & \\\Leftrightarrow & x = \frac{-67}{165} & & \\ & V = \left\{ \frac{-67}{165} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{5}{3})& = & 5x+\frac{3}{4} \\\Leftrightarrow & -12x-\frac{20}{3}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-144}{ \color{blue}{12} }x- \frac{80}{ \color{blue}{12} })& = & (\frac{60}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -144x \color{red}{-80} & = & \color{red}{60x} +9 \\\Leftrightarrow & -144x \color{red}{-80} \color{blue}{+80} \color{blue}{-60x} & = & \color{red}{60x} +9 \color{blue}{-60x} \color{blue}{+80} \\\Leftrightarrow & -144x-60x& = & 9+80 \\\Leftrightarrow & \color{red}{-204} x& = & 89 \\\Leftrightarrow & x = \frac{89}{-204} & & \\\Leftrightarrow & x = \frac{-89}{204} & & \\ & V = \left\{ \frac{-89}{204} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{2}{3})& = & -8x+\frac{6}{11} \\\Leftrightarrow & 35x-\frac{14}{3}& = & -8x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{1155}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 1155x \color{red}{-154} & = & \color{red}{-264x} +18 \\\Leftrightarrow & 1155x \color{red}{-154} \color{blue}{+154} \color{blue}{+264x} & = & \color{red}{-264x} +18 \color{blue}{+264x} \color{blue}{+154} \\\Leftrightarrow & 1155x+264x& = & 18+154 \\\Leftrightarrow & \color{red}{1419} x& = & 172 \\\Leftrightarrow & x = \frac{172}{1419} & & \\\Leftrightarrow & x = \frac{4}{33} & & \\ & V = \left\{ \frac{4}{33} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{2}{7})& = & -7x+\frac{7}{12} \\\Leftrightarrow & 15x-\frac{10}{7}& = & -7x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{1260}{ \color{blue}{84} }x- \frac{120}{ \color{blue}{84} })& = & (\frac{-588}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 1260x \color{red}{-120} & = & \color{red}{-588x} +49 \\\Leftrightarrow & 1260x \color{red}{-120} \color{blue}{+120} \color{blue}{+588x} & = & \color{red}{-588x} +49 \color{blue}{+588x} \color{blue}{+120} \\\Leftrightarrow & 1260x+588x& = & 49+120 \\\Leftrightarrow & \color{red}{1848} x& = & 169 \\\Leftrightarrow & x = \frac{169}{1848} & & \\ & V = \left\{ \frac{169}{1848} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{3}{4})& = & -9x+\frac{3}{8} \\\Leftrightarrow & -25x-\frac{15}{4}& = & -9x+\frac{3}{8} \\ & & & \text{kgv van noemers 4 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-200}{ \color{blue}{8} }x- \frac{30}{ \color{blue}{8} })& = & (\frac{-72}{ \color{blue}{8} }x+ \frac{3}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -200x \color{red}{-30} & = & \color{red}{-72x} +3 \\\Leftrightarrow & -200x \color{red}{-30} \color{blue}{+30} \color{blue}{+72x} & = & \color{red}{-72x} +3 \color{blue}{+72x} \color{blue}{+30} \\\Leftrightarrow & -200x+72x& = & 3+30 \\\Leftrightarrow & \color{red}{-128} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-128} & & \\\Leftrightarrow & x = \frac{-33}{128} & & \\ & V = \left\{ \frac{-33}{128} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{2}{5})& = & 3x+\frac{9}{7} \\\Leftrightarrow & 8x+\frac{4}{5}& = & 3x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{+28} & = & \color{red}{105x} +45 \\\Leftrightarrow & 280x \color{red}{+28} \color{blue}{-28} \color{blue}{-105x} & = & \color{red}{105x} +45 \color{blue}{-105x} \color{blue}{-28} \\\Leftrightarrow & 280x-105x& = & 45-28 \\\Leftrightarrow & \color{red}{175} x& = & 17 \\\Leftrightarrow & x = \frac{17}{175} & & \\ & V = \left\{ \frac{17}{175} \right\} & \\\end{align}\)