Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{4}{3})& = & 9x+\frac{5}{3} \\\Leftrightarrow & 14x+\frac{28}{3}& = & 9x+\frac{5}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{42}{ \color{blue}{3} }x+ \frac{28}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{5}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 42x \color{red}{+28} & = & \color{red}{27x} +5 \\\Leftrightarrow & 42x \color{red}{+28} \color{blue}{-28} \color{blue}{-27x} & = & \color{red}{27x} +5 \color{blue}{-27x} \color{blue}{-28} \\\Leftrightarrow & 42x-27x& = & 5-28 \\\Leftrightarrow & \color{red}{15} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{15} & & \\ & V = \left\{ \frac{-23}{15} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{3}{4})& = & -4x+\frac{3}{2} \\\Leftrightarrow & -15x+\frac{15}{4}& = & -4x+\frac{3}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-60}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{-16}{ \color{blue}{4} }x+ \frac{6}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -60x \color{red}{+15} & = & \color{red}{-16x} +6 \\\Leftrightarrow & -60x \color{red}{+15} \color{blue}{-15} \color{blue}{+16x} & = & \color{red}{-16x} +6 \color{blue}{+16x} \color{blue}{-15} \\\Leftrightarrow & -60x+16x& = & 6-15 \\\Leftrightarrow & \color{red}{-44} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-44} & & \\\Leftrightarrow & x = \frac{9}{44} & & \\ & V = \left\{ \frac{9}{44} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{3}{11})& = & 5x+\frac{9}{4} \\\Leftrightarrow & 12x+\frac{18}{11}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{528}{ \color{blue}{44} }x+ \frac{72}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 528x \color{red}{+72} & = & \color{red}{220x} +99 \\\Leftrightarrow & 528x \color{red}{+72} \color{blue}{-72} \color{blue}{-220x} & = & \color{red}{220x} +99 \color{blue}{-220x} \color{blue}{-72} \\\Leftrightarrow & 528x-220x& = & 99-72 \\\Leftrightarrow & \color{red}{308} x& = & 27 \\\Leftrightarrow & x = \frac{27}{308} & & \\ & V = \left\{ \frac{27}{308} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{5}{11})& = & 6x+\frac{10}{3} \\\Leftrightarrow & 35x+\frac{35}{11}& = & 6x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{1155}{ \color{blue}{33} }x+ \frac{105}{ \color{blue}{33} })& = & (\frac{198}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 1155x \color{red}{+105} & = & \color{red}{198x} +110 \\\Leftrightarrow & 1155x \color{red}{+105} \color{blue}{-105} \color{blue}{-198x} & = & \color{red}{198x} +110 \color{blue}{-198x} \color{blue}{-105} \\\Leftrightarrow & 1155x-198x& = & 110-105 \\\Leftrightarrow & \color{red}{957} x& = & 5 \\\Leftrightarrow & x = \frac{5}{957} & & \\ & V = \left\{ \frac{5}{957} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{5}{2})& = & 4x+\frac{10}{11} \\\Leftrightarrow & -15x-\frac{15}{2}& = & 4x+\frac{10}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-330}{ \color{blue}{22} }x- \frac{165}{ \color{blue}{22} })& = & (\frac{88}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -330x \color{red}{-165} & = & \color{red}{88x} +20 \\\Leftrightarrow & -330x \color{red}{-165} \color{blue}{+165} \color{blue}{-88x} & = & \color{red}{88x} +20 \color{blue}{-88x} \color{blue}{+165} \\\Leftrightarrow & -330x-88x& = & 20+165 \\\Leftrightarrow & \color{red}{-418} x& = & 185 \\\Leftrightarrow & x = \frac{185}{-418} & & \\\Leftrightarrow & x = \frac{-185}{418} & & \\ & V = \left\{ \frac{-185}{418} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{2}{7})& = & 7x+\frac{10}{9} \\\Leftrightarrow & 15x+\frac{6}{7}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{945}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 945x \color{red}{+54} & = & \color{red}{441x} +70 \\\Leftrightarrow & 945x \color{red}{+54} \color{blue}{-54} \color{blue}{-441x} & = & \color{red}{441x} +70 \color{blue}{-441x} \color{blue}{-54} \\\Leftrightarrow & 945x-441x& = & 70-54 \\\Leftrightarrow & \color{red}{504} x& = & 16 \\\Leftrightarrow & x = \frac{16}{504} & & \\\Leftrightarrow & x = \frac{2}{63} & & \\ & V = \left\{ \frac{2}{63} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{2}{9})& = & -9x+\frac{2}{3} \\\Leftrightarrow & 16x-\frac{8}{9}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{144}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 144x \color{red}{-8} & = & \color{red}{-81x} +6 \\\Leftrightarrow & 144x \color{red}{-8} \color{blue}{+8} \color{blue}{+81x} & = & \color{red}{-81x} +6 \color{blue}{+81x} \color{blue}{+8} \\\Leftrightarrow & 144x+81x& = & 6+8 \\\Leftrightarrow & \color{red}{225} x& = & 14 \\\Leftrightarrow & x = \frac{14}{225} & & \\ & V = \left\{ \frac{14}{225} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{2}{5})& = & -7x+\frac{9}{10} \\\Leftrightarrow & -10x-\frac{4}{5}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-100}{ \color{blue}{10} }x- \frac{8}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -100x \color{red}{-8} & = & \color{red}{-70x} +9 \\\Leftrightarrow & -100x \color{red}{-8} \color{blue}{+8} \color{blue}{+70x} & = & \color{red}{-70x} +9 \color{blue}{+70x} \color{blue}{+8} \\\Leftrightarrow & -100x+70x& = & 9+8 \\\Leftrightarrow & \color{red}{-30} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-30} & & \\\Leftrightarrow & x = \frac{-17}{30} & & \\ & V = \left\{ \frac{-17}{30} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{4}{7})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -24x-\frac{24}{7}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-504}{ \color{blue}{21} }x- \frac{72}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -504x \color{red}{-72} & = & \color{red}{-147x} +70 \\\Leftrightarrow & -504x \color{red}{-72} \color{blue}{+72} \color{blue}{+147x} & = & \color{red}{-147x} +70 \color{blue}{+147x} \color{blue}{+72} \\\Leftrightarrow & -504x+147x& = & 70+72 \\\Leftrightarrow & \color{red}{-357} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-357} & & \\\Leftrightarrow & x = \frac{-142}{357} & & \\ & V = \left\{ \frac{-142}{357} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{4}{9})& = & 8x+\frac{6}{5} \\\Leftrightarrow & -21x-\frac{28}{9}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-945}{ \color{blue}{45} }x- \frac{140}{ \color{blue}{45} })& = & (\frac{360}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -945x \color{red}{-140} & = & \color{red}{360x} +54 \\\Leftrightarrow & -945x \color{red}{-140} \color{blue}{+140} \color{blue}{-360x} & = & \color{red}{360x} +54 \color{blue}{-360x} \color{blue}{+140} \\\Leftrightarrow & -945x-360x& = & 54+140 \\\Leftrightarrow & \color{red}{-1305} x& = & 194 \\\Leftrightarrow & x = \frac{194}{-1305} & & \\\Leftrightarrow & x = \frac{-194}{1305} & & \\ & V = \left\{ \frac{-194}{1305} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{5}{4})& = & 7x+\frac{7}{5} \\\Leftrightarrow & 12x-\frac{15}{4}& = & 7x+\frac{7}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{240}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{28}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 240x \color{red}{-75} & = & \color{red}{140x} +28 \\\Leftrightarrow & 240x \color{red}{-75} \color{blue}{+75} \color{blue}{-140x} & = & \color{red}{140x} +28 \color{blue}{-140x} \color{blue}{+75} \\\Leftrightarrow & 240x-140x& = & 28+75 \\\Leftrightarrow & \color{red}{100} x& = & 103 \\\Leftrightarrow & x = \frac{103}{100} & & \\ & V = \left\{ \frac{103}{100} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{2}{5})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -6x-\frac{4}{5}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x- \frac{12}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{-12} & = & \color{red}{105x} +40 \\\Leftrightarrow & -90x \color{red}{-12} \color{blue}{+12} \color{blue}{-105x} & = & \color{red}{105x} +40 \color{blue}{-105x} \color{blue}{+12} \\\Leftrightarrow & -90x-105x& = & 40+12 \\\Leftrightarrow & \color{red}{-195} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-195} & & \\\Leftrightarrow & x = \frac{-4}{15} & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)