Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{2}{5})& = & 8x+\frac{6}{5} \\\Leftrightarrow & -18x+\frac{12}{5}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-90}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{40}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -90x \color{red}{+12} & = & \color{red}{40x} +6 \\\Leftrightarrow & -90x \color{red}{+12} \color{blue}{-12} \color{blue}{-40x} & = & \color{red}{40x} +6 \color{blue}{-40x} \color{blue}{-12} \\\Leftrightarrow & -90x-40x& = & 6-12 \\\Leftrightarrow & \color{red}{-130} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-130} & & \\\Leftrightarrow & x = \frac{3}{65} & & \\ & V = \left\{ \frac{3}{65} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{3}{5})& = & 9x+\frac{3}{2} \\\Leftrightarrow & -8x-\frac{12}{5}& = & 9x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-80}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{90}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -80x \color{red}{-24} & = & \color{red}{90x} +15 \\\Leftrightarrow & -80x \color{red}{-24} \color{blue}{+24} \color{blue}{-90x} & = & \color{red}{90x} +15 \color{blue}{-90x} \color{blue}{+24} \\\Leftrightarrow & -80x-90x& = & 15+24 \\\Leftrightarrow & \color{red}{-170} x& = & 39 \\\Leftrightarrow & x = \frac{39}{-170} & & \\\Leftrightarrow & x = \frac{-39}{170} & & \\ & V = \left\{ \frac{-39}{170} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{2}{5})& = & -4x+\frac{2}{3} \\\Leftrightarrow & -15x+\frac{6}{5}& = & -4x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-225}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} })& = & (\frac{-60}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -225x \color{red}{+18} & = & \color{red}{-60x} +10 \\\Leftrightarrow & -225x \color{red}{+18} \color{blue}{-18} \color{blue}{+60x} & = & \color{red}{-60x} +10 \color{blue}{+60x} \color{blue}{-18} \\\Leftrightarrow & -225x+60x& = & 10-18 \\\Leftrightarrow & \color{red}{-165} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-165} & & \\\Leftrightarrow & x = \frac{8}{165} & & \\ & V = \left\{ \frac{8}{165} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{5}{7})& = & 9x+\frac{10}{9} \\\Leftrightarrow & -18x+\frac{30}{7}& = & 9x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1134}{ \color{blue}{63} }x+ \frac{270}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1134x \color{red}{+270} & = & \color{red}{567x} +70 \\\Leftrightarrow & -1134x \color{red}{+270} \color{blue}{-270} \color{blue}{-567x} & = & \color{red}{567x} +70 \color{blue}{-567x} \color{blue}{-270} \\\Leftrightarrow & -1134x-567x& = & 70-270 \\\Leftrightarrow & \color{red}{-1701} x& = & -200 \\\Leftrightarrow & x = \frac{-200}{-1701} & & \\\Leftrightarrow & x = \frac{200}{1701} & & \\ & V = \left\{ \frac{200}{1701} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{4}{5})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 6x-\frac{8}{5}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x- \frac{16}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{-16} & = & \color{red}{50x} +15 \\\Leftrightarrow & 60x \color{red}{-16} \color{blue}{+16} \color{blue}{-50x} & = & \color{red}{50x} +15 \color{blue}{-50x} \color{blue}{+16} \\\Leftrightarrow & 60x-50x& = & 15+16 \\\Leftrightarrow & \color{red}{10} x& = & 31 \\\Leftrightarrow & x = \frac{31}{10} & & \\ & V = \left\{ \frac{31}{10} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{3}{8})& = & -9x+\frac{10}{3} \\\Leftrightarrow & 14x-\frac{21}{8}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{336}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{-216}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 336x \color{red}{-63} & = & \color{red}{-216x} +80 \\\Leftrightarrow & 336x \color{red}{-63} \color{blue}{+63} \color{blue}{+216x} & = & \color{red}{-216x} +80 \color{blue}{+216x} \color{blue}{+63} \\\Leftrightarrow & 336x+216x& = & 80+63 \\\Leftrightarrow & \color{red}{552} x& = & 143 \\\Leftrightarrow & x = \frac{143}{552} & & \\ & V = \left\{ \frac{143}{552} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{3}{8})& = & 3x+\frac{9}{2} \\\Leftrightarrow & -14x-\frac{21}{8}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-112}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{24}{ \color{blue}{8} }x+ \frac{36}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -112x \color{red}{-21} & = & \color{red}{24x} +36 \\\Leftrightarrow & -112x \color{red}{-21} \color{blue}{+21} \color{blue}{-24x} & = & \color{red}{24x} +36 \color{blue}{-24x} \color{blue}{+21} \\\Leftrightarrow & -112x-24x& = & 36+21 \\\Leftrightarrow & \color{red}{-136} x& = & 57 \\\Leftrightarrow & x = \frac{57}{-136} & & \\\Leftrightarrow & x = \frac{-57}{136} & & \\ & V = \left\{ \frac{-57}{136} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{5}{3})& = & 3x+\frac{8}{7} \\\Leftrightarrow & 35x-\frac{35}{3}& = & 3x+\frac{8}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{735}{ \color{blue}{21} }x- \frac{245}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 735x \color{red}{-245} & = & \color{red}{63x} +24 \\\Leftrightarrow & 735x \color{red}{-245} \color{blue}{+245} \color{blue}{-63x} & = & \color{red}{63x} +24 \color{blue}{-63x} \color{blue}{+245} \\\Leftrightarrow & 735x-63x& = & 24+245 \\\Leftrightarrow & \color{red}{672} x& = & 269 \\\Leftrightarrow & x = \frac{269}{672} & & \\ & V = \left\{ \frac{269}{672} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{3}{8})& = & -2x+\frac{9}{7} \\\Leftrightarrow & 21x-\frac{21}{8}& = & -2x+\frac{9}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1176}{ \color{blue}{56} }x- \frac{147}{ \color{blue}{56} })& = & (\frac{-112}{ \color{blue}{56} }x+ \frac{72}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1176x \color{red}{-147} & = & \color{red}{-112x} +72 \\\Leftrightarrow & 1176x \color{red}{-147} \color{blue}{+147} \color{blue}{+112x} & = & \color{red}{-112x} +72 \color{blue}{+112x} \color{blue}{+147} \\\Leftrightarrow & 1176x+112x& = & 72+147 \\\Leftrightarrow & \color{red}{1288} x& = & 219 \\\Leftrightarrow & x = \frac{219}{1288} & & \\ & V = \left\{ \frac{219}{1288} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{5}{3})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 20x+\frac{20}{3}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x+ \frac{40}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{+40} & = & \color{red}{42x} +9 \\\Leftrightarrow & 120x \color{red}{+40} \color{blue}{-40} \color{blue}{-42x} & = & \color{red}{42x} +9 \color{blue}{-42x} \color{blue}{-40} \\\Leftrightarrow & 120x-42x& = & 9-40 \\\Leftrightarrow & \color{red}{78} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{78} & & \\ & V = \left\{ \frac{-31}{78} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{3}{7})& = & -9x+\frac{4}{3} \\\Leftrightarrow & 4x-\frac{6}{7}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{-18} & = & \color{red}{-189x} +28 \\\Leftrightarrow & 84x \color{red}{-18} \color{blue}{+18} \color{blue}{+189x} & = & \color{red}{-189x} +28 \color{blue}{+189x} \color{blue}{+18} \\\Leftrightarrow & 84x+189x& = & 28+18 \\\Leftrightarrow & \color{red}{273} x& = & 46 \\\Leftrightarrow & x = \frac{46}{273} & & \\ & V = \left\{ \frac{46}{273} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{2}{11})& = & -7x+\frac{9}{10} \\\Leftrightarrow & -16x-\frac{8}{11}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1760}{ \color{blue}{110} }x- \frac{80}{ \color{blue}{110} })& = & (\frac{-770}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1760x \color{red}{-80} & = & \color{red}{-770x} +99 \\\Leftrightarrow & -1760x \color{red}{-80} \color{blue}{+80} \color{blue}{+770x} & = & \color{red}{-770x} +99 \color{blue}{+770x} \color{blue}{+80} \\\Leftrightarrow & -1760x+770x& = & 99+80 \\\Leftrightarrow & \color{red}{-990} x& = & 179 \\\Leftrightarrow & x = \frac{179}{-990} & & \\\Leftrightarrow & x = \frac{-179}{990} & & \\ & V = \left\{ \frac{-179}{990} \right\} & \\\end{align}\)