Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{2}{5})& = & -7x+\frac{3}{10} \\\Leftrightarrow & -10x-\frac{4}{5}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-100}{ \color{blue}{10} }x- \frac{8}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -100x \color{red}{-8} & = & \color{red}{-70x} +3 \\\Leftrightarrow & -100x \color{red}{-8} \color{blue}{+8} \color{blue}{+70x} & = & \color{red}{-70x} +3 \color{blue}{+70x} \color{blue}{+8} \\\Leftrightarrow & -100x+70x& = & 3+8 \\\Leftrightarrow & \color{red}{-30} x& = & 11 \\\Leftrightarrow & x = \frac{11}{-30} & & \\\Leftrightarrow & x = \frac{-11}{30} & & \\ & V = \left\{ \frac{-11}{30} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{4}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -6x+\frac{12}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-198}{ \color{blue}{33} }x+ \frac{36}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -198x \color{red}{+36} & = & \color{red}{231x} +22 \\\Leftrightarrow & -198x \color{red}{+36} \color{blue}{-36} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{-36} \\\Leftrightarrow & -198x-231x& = & 22-36 \\\Leftrightarrow & \color{red}{-429} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-429} & & \\\Leftrightarrow & x = \frac{14}{429} & & \\ & V = \left\{ \frac{14}{429} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{2}{3})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -12x-\frac{8}{3}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{-40} & = & \color{red}{-75x} +18 \\\Leftrightarrow & -180x \color{red}{-40} \color{blue}{+40} \color{blue}{+75x} & = & \color{red}{-75x} +18 \color{blue}{+75x} \color{blue}{+40} \\\Leftrightarrow & -180x+75x& = & 18+40 \\\Leftrightarrow & \color{red}{-105} x& = & 58 \\\Leftrightarrow & x = \frac{58}{-105} & & \\\Leftrightarrow & x = \frac{-58}{105} & & \\ & V = \left\{ \frac{-58}{105} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{4}{11})& = & 7x+\frac{4}{9} \\\Leftrightarrow & -6x-\frac{12}{11}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-594}{ \color{blue}{99} }x- \frac{108}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -594x \color{red}{-108} & = & \color{red}{693x} +44 \\\Leftrightarrow & -594x \color{red}{-108} \color{blue}{+108} \color{blue}{-693x} & = & \color{red}{693x} +44 \color{blue}{-693x} \color{blue}{+108} \\\Leftrightarrow & -594x-693x& = & 44+108 \\\Leftrightarrow & \color{red}{-1287} x& = & 152 \\\Leftrightarrow & x = \frac{152}{-1287} & & \\\Leftrightarrow & x = \frac{-152}{1287} & & \\ & V = \left\{ \frac{-152}{1287} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{1}{3})& = & -9x+\frac{6}{11} \\\Leftrightarrow & 28x-\frac{7}{3}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{924}{ \color{blue}{33} }x- \frac{77}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 924x \color{red}{-77} & = & \color{red}{-297x} +18 \\\Leftrightarrow & 924x \color{red}{-77} \color{blue}{+77} \color{blue}{+297x} & = & \color{red}{-297x} +18 \color{blue}{+297x} \color{blue}{+77} \\\Leftrightarrow & 924x+297x& = & 18+77 \\\Leftrightarrow & \color{red}{1221} x& = & 95 \\\Leftrightarrow & x = \frac{95}{1221} & & \\ & V = \left\{ \frac{95}{1221} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+1)& = & -6x+\frac{8}{5} \\\Leftrightarrow & 25x-5& = & -6x+\frac{8}{5} \\ & & & \text{kgv van noemers 1 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{125}{ \color{blue}{5} }x- \frac{25}{ \color{blue}{5} })& = & (\frac{-30}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 125x \color{red}{-25} & = & \color{red}{-30x} +8 \\\Leftrightarrow & 125x \color{red}{-25} \color{blue}{+25} \color{blue}{+30x} & = & \color{red}{-30x} +8 \color{blue}{+30x} \color{blue}{+25} \\\Leftrightarrow & 125x+30x& = & 8+25 \\\Leftrightarrow & \color{red}{155} x& = & 33 \\\Leftrightarrow & x = \frac{33}{155} & & \\ & V = \left\{ \frac{33}{155} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{4}{7})& = & -9x+\frac{10}{3} \\\Leftrightarrow & 10x-\frac{20}{7}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{-60} & = & \color{red}{-189x} +70 \\\Leftrightarrow & 210x \color{red}{-60} \color{blue}{+60} \color{blue}{+189x} & = & \color{red}{-189x} +70 \color{blue}{+189x} \color{blue}{+60} \\\Leftrightarrow & 210x+189x& = & 70+60 \\\Leftrightarrow & \color{red}{399} x& = & 130 \\\Leftrightarrow & x = \frac{130}{399} & & \\ & V = \left\{ \frac{130}{399} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{4}{5})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 18x-\frac{24}{5}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x- \frac{72}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{-72} & = & \color{red}{105x} +40 \\\Leftrightarrow & 270x \color{red}{-72} \color{blue}{+72} \color{blue}{-105x} & = & \color{red}{105x} +40 \color{blue}{-105x} \color{blue}{+72} \\\Leftrightarrow & 270x-105x& = & 40+72 \\\Leftrightarrow & \color{red}{165} x& = & 112 \\\Leftrightarrow & x = \frac{112}{165} & & \\ & V = \left\{ \frac{112}{165} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{5}{7})& = & -7x+\frac{6}{7} \\\Leftrightarrow & -16x-\frac{20}{7}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-112}{ \color{blue}{7} }x- \frac{20}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -112x \color{red}{-20} & = & \color{red}{-49x} +6 \\\Leftrightarrow & -112x \color{red}{-20} \color{blue}{+20} \color{blue}{+49x} & = & \color{red}{-49x} +6 \color{blue}{+49x} \color{blue}{+20} \\\Leftrightarrow & -112x+49x& = & 6+20 \\\Leftrightarrow & \color{red}{-63} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-63} & & \\\Leftrightarrow & x = \frac{-26}{63} & & \\ & V = \left\{ \frac{-26}{63} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{5}{11})& = & -6x+\frac{4}{7} \\\Leftrightarrow & 35x+\frac{35}{11}& = & -6x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2695}{ \color{blue}{77} }x+ \frac{245}{ \color{blue}{77} })& = & (\frac{-462}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2695x \color{red}{+245} & = & \color{red}{-462x} +44 \\\Leftrightarrow & 2695x \color{red}{+245} \color{blue}{-245} \color{blue}{+462x} & = & \color{red}{-462x} +44 \color{blue}{+462x} \color{blue}{-245} \\\Leftrightarrow & 2695x+462x& = & 44-245 \\\Leftrightarrow & \color{red}{3157} x& = & -201 \\\Leftrightarrow & x = \frac{-201}{3157} & & \\ & V = \left\{ \frac{-201}{3157} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{3}{4})& = & -4x+\frac{3}{2} \\\Leftrightarrow & -15x-\frac{15}{4}& = & -4x+\frac{3}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-60}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{-16}{ \color{blue}{4} }x+ \frac{6}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -60x \color{red}{-15} & = & \color{red}{-16x} +6 \\\Leftrightarrow & -60x \color{red}{-15} \color{blue}{+15} \color{blue}{+16x} & = & \color{red}{-16x} +6 \color{blue}{+16x} \color{blue}{+15} \\\Leftrightarrow & -60x+16x& = & 6+15 \\\Leftrightarrow & \color{red}{-44} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-44} & & \\\Leftrightarrow & x = \frac{-21}{44} & & \\ & V = \left\{ \frac{-21}{44} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{3}{11})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 24x-\frac{18}{11}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{792}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 792x \color{red}{-54} & = & \color{red}{-165x} +22 \\\Leftrightarrow & 792x \color{red}{-54} \color{blue}{+54} \color{blue}{+165x} & = & \color{red}{-165x} +22 \color{blue}{+165x} \color{blue}{+54} \\\Leftrightarrow & 792x+165x& = & 22+54 \\\Leftrightarrow & \color{red}{957} x& = & 76 \\\Leftrightarrow & x = \frac{76}{957} & & \\ & V = \left\{ \frac{76}{957} \right\} & \\\end{align}\)