Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{3}{5})& = & -7x+\frac{5}{12} \\\Leftrightarrow & -16x-\frac{12}{5}& = & -7x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-960}{ \color{blue}{60} }x- \frac{144}{ \color{blue}{60} })& = & (\frac{-420}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -960x \color{red}{-144} & = & \color{red}{-420x} +25 \\\Leftrightarrow & -960x \color{red}{-144} \color{blue}{+144} \color{blue}{+420x} & = & \color{red}{-420x} +25 \color{blue}{+420x} \color{blue}{+144} \\\Leftrightarrow & -960x+420x& = & 25+144 \\\Leftrightarrow & \color{red}{-540} x& = & 169 \\\Leftrightarrow & x = \frac{169}{-540} & & \\\Leftrightarrow & x = \frac{-169}{540} & & \\ & V = \left\{ \frac{-169}{540} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{4}{5})& = & 7x+\frac{8}{11} \\\Leftrightarrow & 30x+\frac{24}{5}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{+264} & = & \color{red}{385x} +40 \\\Leftrightarrow & 1650x \color{red}{+264} \color{blue}{-264} \color{blue}{-385x} & = & \color{red}{385x} +40 \color{blue}{-385x} \color{blue}{-264} \\\Leftrightarrow & 1650x-385x& = & 40-264 \\\Leftrightarrow & \color{red}{1265} x& = & -224 \\\Leftrightarrow & x = \frac{-224}{1265} & & \\ & V = \left\{ \frac{-224}{1265} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{2}{7})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -10x-\frac{10}{7}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{-110} & = & \color{red}{539x} +42 \\\Leftrightarrow & -770x \color{red}{-110} \color{blue}{+110} \color{blue}{-539x} & = & \color{red}{539x} +42 \color{blue}{-539x} \color{blue}{+110} \\\Leftrightarrow & -770x-539x& = & 42+110 \\\Leftrightarrow & \color{red}{-1309} x& = & 152 \\\Leftrightarrow & x = \frac{152}{-1309} & & \\\Leftrightarrow & x = \frac{-152}{1309} & & \\ & V = \left\{ \frac{-152}{1309} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{3}{5})& = & -5x+\frac{4}{5} \\\Leftrightarrow & 18x-\frac{18}{5}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{90}{ \color{blue}{5} }x- \frac{18}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 90x \color{red}{-18} & = & \color{red}{-25x} +4 \\\Leftrightarrow & 90x \color{red}{-18} \color{blue}{+18} \color{blue}{+25x} & = & \color{red}{-25x} +4 \color{blue}{+25x} \color{blue}{+18} \\\Leftrightarrow & 90x+25x& = & 4+18 \\\Leftrightarrow & \color{red}{115} x& = & 22 \\\Leftrightarrow & x = \frac{22}{115} & & \\ & V = \left\{ \frac{22}{115} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{5}{7})& = & 9x+\frac{8}{5} \\\Leftrightarrow & 4x+\frac{10}{7}& = & 9x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{+50} & = & \color{red}{315x} +56 \\\Leftrightarrow & 140x \color{red}{+50} \color{blue}{-50} \color{blue}{-315x} & = & \color{red}{315x} +56 \color{blue}{-315x} \color{blue}{-50} \\\Leftrightarrow & 140x-315x& = & 56-50 \\\Leftrightarrow & \color{red}{-175} x& = & 6 \\\Leftrightarrow & x = \frac{6}{-175} & & \\\Leftrightarrow & x = \frac{-6}{175} & & \\ & V = \left\{ \frac{-6}{175} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{4}{7})& = & 7x+\frac{8}{9} \\\Leftrightarrow & -30x+\frac{24}{7}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1890}{ \color{blue}{63} }x+ \frac{216}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1890x \color{red}{+216} & = & \color{red}{441x} +56 \\\Leftrightarrow & -1890x \color{red}{+216} \color{blue}{-216} \color{blue}{-441x} & = & \color{red}{441x} +56 \color{blue}{-441x} \color{blue}{-216} \\\Leftrightarrow & -1890x-441x& = & 56-216 \\\Leftrightarrow & \color{red}{-2331} x& = & -160 \\\Leftrightarrow & x = \frac{-160}{-2331} & & \\\Leftrightarrow & x = \frac{160}{2331} & & \\ & V = \left\{ \frac{160}{2331} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{3}{8})& = & -3x+\frac{10}{7} \\\Leftrightarrow & 14x-\frac{21}{8}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{784}{ \color{blue}{56} }x- \frac{147}{ \color{blue}{56} })& = & (\frac{-168}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 784x \color{red}{-147} & = & \color{red}{-168x} +80 \\\Leftrightarrow & 784x \color{red}{-147} \color{blue}{+147} \color{blue}{+168x} & = & \color{red}{-168x} +80 \color{blue}{+168x} \color{blue}{+147} \\\Leftrightarrow & 784x+168x& = & 80+147 \\\Leftrightarrow & \color{red}{952} x& = & 227 \\\Leftrightarrow & x = \frac{227}{952} & & \\ & V = \left\{ \frac{227}{952} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{2}{3})& = & -8x+\frac{6}{5} \\\Leftrightarrow & -21x+\frac{14}{3}& = & -8x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-315}{ \color{blue}{15} }x+ \frac{70}{ \color{blue}{15} })& = & (\frac{-120}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -315x \color{red}{+70} & = & \color{red}{-120x} +18 \\\Leftrightarrow & -315x \color{red}{+70} \color{blue}{-70} \color{blue}{+120x} & = & \color{red}{-120x} +18 \color{blue}{+120x} \color{blue}{-70} \\\Leftrightarrow & -315x+120x& = & 18-70 \\\Leftrightarrow & \color{red}{-195} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{-195} & & \\\Leftrightarrow & x = \frac{4}{15} & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{5}{6})& = & -8x+\frac{8}{3} \\\Leftrightarrow & 35x+\frac{35}{6}& = & -8x+\frac{8}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{210}{ \color{blue}{6} }x+ \frac{35}{ \color{blue}{6} })& = & (\frac{-48}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 210x \color{red}{+35} & = & \color{red}{-48x} +16 \\\Leftrightarrow & 210x \color{red}{+35} \color{blue}{-35} \color{blue}{+48x} & = & \color{red}{-48x} +16 \color{blue}{+48x} \color{blue}{-35} \\\Leftrightarrow & 210x+48x& = & 16-35 \\\Leftrightarrow & \color{red}{258} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{258} & & \\ & V = \left\{ \frac{-19}{258} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{3}{5})& = & 3x+\frac{10}{9} \\\Leftrightarrow & 8x-\frac{12}{5}& = & 3x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{360}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{135}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 360x \color{red}{-108} & = & \color{red}{135x} +50 \\\Leftrightarrow & 360x \color{red}{-108} \color{blue}{+108} \color{blue}{-135x} & = & \color{red}{135x} +50 \color{blue}{-135x} \color{blue}{+108} \\\Leftrightarrow & 360x-135x& = & 50+108 \\\Leftrightarrow & \color{red}{225} x& = & 158 \\\Leftrightarrow & x = \frac{158}{225} & & \\ & V = \left\{ \frac{158}{225} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{2}{11})& = & -4x+\frac{4}{11} \\\Leftrightarrow & 15x+\frac{10}{11}& = & -4x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{165}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} })& = & (\frac{-44}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 165x \color{red}{+10} & = & \color{red}{-44x} +4 \\\Leftrightarrow & 165x \color{red}{+10} \color{blue}{-10} \color{blue}{+44x} & = & \color{red}{-44x} +4 \color{blue}{+44x} \color{blue}{-10} \\\Leftrightarrow & 165x+44x& = & 4-10 \\\Leftrightarrow & \color{red}{209} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{209} & & \\ & V = \left\{ \frac{-6}{209} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{2}{3})& = & -3x+\frac{9}{8} \\\Leftrightarrow & -14x+\frac{14}{3}& = & -3x+\frac{9}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-336}{ \color{blue}{24} }x+ \frac{112}{ \color{blue}{24} })& = & (\frac{-72}{ \color{blue}{24} }x+ \frac{27}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -336x \color{red}{+112} & = & \color{red}{-72x} +27 \\\Leftrightarrow & -336x \color{red}{+112} \color{blue}{-112} \color{blue}{+72x} & = & \color{red}{-72x} +27 \color{blue}{+72x} \color{blue}{-112} \\\Leftrightarrow & -336x+72x& = & 27-112 \\\Leftrightarrow & \color{red}{-264} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{-264} & & \\\Leftrightarrow & x = \frac{85}{264} & & \\ & V = \left\{ \frac{85}{264} \right\} & \\\end{align}\)