Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{5}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 18x+\frac{30}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{594}{ \color{blue}{33} }x+ \frac{90}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 594x \color{red}{+90} & = & \color{red}{231x} +22 \\\Leftrightarrow & 594x \color{red}{+90} \color{blue}{-90} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{-90} \\\Leftrightarrow & 594x-231x& = & 22-90 \\\Leftrightarrow & \color{red}{363} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{363} & & \\ & V = \left\{ \frac{-68}{363} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{3}{8})& = & -9x+\frac{4}{7} \\\Leftrightarrow & -35x-\frac{21}{8}& = & -9x+\frac{4}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1960}{ \color{blue}{56} }x- \frac{147}{ \color{blue}{56} })& = & (\frac{-504}{ \color{blue}{56} }x+ \frac{32}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1960x \color{red}{-147} & = & \color{red}{-504x} +32 \\\Leftrightarrow & -1960x \color{red}{-147} \color{blue}{+147} \color{blue}{+504x} & = & \color{red}{-504x} +32 \color{blue}{+504x} \color{blue}{+147} \\\Leftrightarrow & -1960x+504x& = & 32+147 \\\Leftrightarrow & \color{red}{-1456} x& = & 179 \\\Leftrightarrow & x = \frac{179}{-1456} & & \\\Leftrightarrow & x = \frac{-179}{1456} & & \\ & V = \left\{ \frac{-179}{1456} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{3}{7})& = & 9x+\frac{3}{10} \\\Leftrightarrow & -8x-\frac{6}{7}& = & 9x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-560}{ \color{blue}{70} }x- \frac{60}{ \color{blue}{70} })& = & (\frac{630}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -560x \color{red}{-60} & = & \color{red}{630x} +21 \\\Leftrightarrow & -560x \color{red}{-60} \color{blue}{+60} \color{blue}{-630x} & = & \color{red}{630x} +21 \color{blue}{-630x} \color{blue}{+60} \\\Leftrightarrow & -560x-630x& = & 21+60 \\\Leftrightarrow & \color{red}{-1190} x& = & 81 \\\Leftrightarrow & x = \frac{81}{-1190} & & \\\Leftrightarrow & x = \frac{-81}{1190} & & \\ & V = \left\{ \frac{-81}{1190} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+1)& = & 8x+\frac{2}{5} \\\Leftrightarrow & -21x-7& = & 8x+\frac{2}{5} \\ & & & \text{kgv van noemers 1 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-105}{ \color{blue}{5} }x- \frac{35}{ \color{blue}{5} })& = & (\frac{40}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -105x \color{red}{-35} & = & \color{red}{40x} +2 \\\Leftrightarrow & -105x \color{red}{-35} \color{blue}{+35} \color{blue}{-40x} & = & \color{red}{40x} +2 \color{blue}{-40x} \color{blue}{+35} \\\Leftrightarrow & -105x-40x& = & 2+35 \\\Leftrightarrow & \color{red}{-145} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-145} & & \\\Leftrightarrow & x = \frac{-37}{145} & & \\ & V = \left\{ \frac{-37}{145} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{2}{7})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -9x-\frac{6}{7}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-63}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -63x \color{red}{-6} & = & \color{red}{-35x} +2 \\\Leftrightarrow & -63x \color{red}{-6} \color{blue}{+6} \color{blue}{+35x} & = & \color{red}{-35x} +2 \color{blue}{+35x} \color{blue}{+6} \\\Leftrightarrow & -63x+35x& = & 2+6 \\\Leftrightarrow & \color{red}{-28} x& = & 8 \\\Leftrightarrow & x = \frac{8}{-28} & & \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{3}{4})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -25x+\frac{15}{4}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1100}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{24}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1100x \color{red}{+165} & = & \color{red}{-220x} +24 \\\Leftrightarrow & -1100x \color{red}{+165} \color{blue}{-165} \color{blue}{+220x} & = & \color{red}{-220x} +24 \color{blue}{+220x} \color{blue}{-165} \\\Leftrightarrow & -1100x+220x& = & 24-165 \\\Leftrightarrow & \color{red}{-880} x& = & -141 \\\Leftrightarrow & x = \frac{-141}{-880} & & \\\Leftrightarrow & x = \frac{141}{880} & & \\ & V = \left\{ \frac{141}{880} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{2}{5})& = & 5x+\frac{3}{4} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{240}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 240x \color{red}{-48} & = & \color{red}{100x} +15 \\\Leftrightarrow & 240x \color{red}{-48} \color{blue}{+48} \color{blue}{-100x} & = & \color{red}{100x} +15 \color{blue}{-100x} \color{blue}{+48} \\\Leftrightarrow & 240x-100x& = & 15+48 \\\Leftrightarrow & \color{red}{140} x& = & 63 \\\Leftrightarrow & x = \frac{63}{140} & & \\\Leftrightarrow & x = \frac{9}{20} & & \\ & V = \left\{ \frac{9}{20} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{4}{5})& = & 5x+\frac{2}{9} \\\Leftrightarrow & 6x+\frac{12}{5}& = & 5x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{270}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 270x \color{red}{+108} & = & \color{red}{225x} +10 \\\Leftrightarrow & 270x \color{red}{+108} \color{blue}{-108} \color{blue}{-225x} & = & \color{red}{225x} +10 \color{blue}{-225x} \color{blue}{-108} \\\Leftrightarrow & 270x-225x& = & 10-108 \\\Leftrightarrow & \color{red}{45} x& = & -98 \\\Leftrightarrow & x = \frac{-98}{45} & & \\ & V = \left\{ \frac{-98}{45} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{5}{11})& = & 2x+\frac{10}{7} \\\Leftrightarrow & 35x-\frac{35}{11}& = & 2x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2695}{ \color{blue}{77} }x- \frac{245}{ \color{blue}{77} })& = & (\frac{154}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2695x \color{red}{-245} & = & \color{red}{154x} +110 \\\Leftrightarrow & 2695x \color{red}{-245} \color{blue}{+245} \color{blue}{-154x} & = & \color{red}{154x} +110 \color{blue}{-154x} \color{blue}{+245} \\\Leftrightarrow & 2695x-154x& = & 110+245 \\\Leftrightarrow & \color{red}{2541} x& = & 355 \\\Leftrightarrow & x = \frac{355}{2541} & & \\ & V = \left\{ \frac{355}{2541} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{5}{4})& = & -8x+\frac{2}{3} \\\Leftrightarrow & -15x-\frac{15}{4}& = & -8x+\frac{2}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-180}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{-96}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -180x \color{red}{-45} & = & \color{red}{-96x} +8 \\\Leftrightarrow & -180x \color{red}{-45} \color{blue}{+45} \color{blue}{+96x} & = & \color{red}{-96x} +8 \color{blue}{+96x} \color{blue}{+45} \\\Leftrightarrow & -180x+96x& = & 8+45 \\\Leftrightarrow & \color{red}{-84} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-84} & & \\\Leftrightarrow & x = \frac{-53}{84} & & \\ & V = \left\{ \frac{-53}{84} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{7})& = & -5x+\frac{10}{7} \\\Leftrightarrow & -4x+\frac{4}{7}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-28}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -28x \color{red}{+4} & = & \color{red}{-35x} +10 \\\Leftrightarrow & -28x \color{red}{+4} \color{blue}{-4} \color{blue}{+35x} & = & \color{red}{-35x} +10 \color{blue}{+35x} \color{blue}{-4} \\\Leftrightarrow & -28x+35x& = & 10-4 \\\Leftrightarrow & \color{red}{7} x& = & 6 \\\Leftrightarrow & x = \frac{6}{7} & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{3}{11})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 12x+\frac{18}{11}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{132}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 132x \color{red}{+18} & = & \color{red}{55x} +6 \\\Leftrightarrow & 132x \color{red}{+18} \color{blue}{-18} \color{blue}{-55x} & = & \color{red}{55x} +6 \color{blue}{-55x} \color{blue}{-18} \\\Leftrightarrow & 132x-55x& = & 6-18 \\\Leftrightarrow & \color{red}{77} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{77} & & \\ & V = \left\{ \frac{-12}{77} \right\} & \\\end{align}\)