Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{2}{11})& = & -4x+\frac{10}{11} \\\Leftrightarrow & -15x+\frac{10}{11}& = & -4x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-165}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} })& = & (\frac{-44}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -165x \color{red}{+10} & = & \color{red}{-44x} +10 \\\Leftrightarrow & -165x \color{red}{+10} \color{blue}{-10} \color{blue}{+44x} & = & \color{red}{-44x} +10 \color{blue}{+44x} \color{blue}{-10} \\\Leftrightarrow & -165x+44x& = & 10-10 \\\Leftrightarrow & \color{red}{-121} x& = & 0 \\\Leftrightarrow & x = \frac{0}{-121} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{2}{5})& = & 5x+\frac{10}{11} \\\Leftrightarrow & 6x+\frac{6}{5}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{+66} & = & \color{red}{275x} +50 \\\Leftrightarrow & 330x \color{red}{+66} \color{blue}{-66} \color{blue}{-275x} & = & \color{red}{275x} +50 \color{blue}{-275x} \color{blue}{-66} \\\Leftrightarrow & 330x-275x& = & 50-66 \\\Leftrightarrow & \color{red}{55} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{55} & & \\ & V = \left\{ \frac{-16}{55} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{2}{5})& = & -5x+\frac{3}{7} \\\Leftrightarrow & 6x-\frac{6}{5}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{42}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-42} & = & \color{red}{-175x} +15 \\\Leftrightarrow & 210x \color{red}{-42} \color{blue}{+42} \color{blue}{+175x} & = & \color{red}{-175x} +15 \color{blue}{+175x} \color{blue}{+42} \\\Leftrightarrow & 210x+175x& = & 15+42 \\\Leftrightarrow & \color{red}{385} x& = & 57 \\\Leftrightarrow & x = \frac{57}{385} & & \\ & V = \left\{ \frac{57}{385} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{5}{8})& = & -5x+\frac{2}{9} \\\Leftrightarrow & -25x-\frac{25}{8}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1800}{ \color{blue}{72} }x- \frac{225}{ \color{blue}{72} })& = & (\frac{-360}{ \color{blue}{72} }x+ \frac{16}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1800x \color{red}{-225} & = & \color{red}{-360x} +16 \\\Leftrightarrow & -1800x \color{red}{-225} \color{blue}{+225} \color{blue}{+360x} & = & \color{red}{-360x} +16 \color{blue}{+360x} \color{blue}{+225} \\\Leftrightarrow & -1800x+360x& = & 16+225 \\\Leftrightarrow & \color{red}{-1440} x& = & 241 \\\Leftrightarrow & x = \frac{241}{-1440} & & \\\Leftrightarrow & x = \frac{-241}{1440} & & \\ & V = \left\{ \frac{-241}{1440} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{5}{6})& = & -9x+\frac{3}{2} \\\Leftrightarrow & 35x+\frac{35}{6}& = & -9x+\frac{3}{2} \\ & & & \text{kgv van noemers 6 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{210}{ \color{blue}{6} }x+ \frac{35}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 210x \color{red}{+35} & = & \color{red}{-54x} +9 \\\Leftrightarrow & 210x \color{red}{+35} \color{blue}{-35} \color{blue}{+54x} & = & \color{red}{-54x} +9 \color{blue}{+54x} \color{blue}{-35} \\\Leftrightarrow & 210x+54x& = & 9-35 \\\Leftrightarrow & \color{red}{264} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{264} & & \\\Leftrightarrow & x = \frac{-13}{132} & & \\ & V = \left\{ \frac{-13}{132} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{7})& = & 9x+\frac{4}{3} \\\Leftrightarrow & -20x-\frac{16}{7}& = & 9x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x- \frac{48}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{-48} & = & \color{red}{189x} +28 \\\Leftrightarrow & -420x \color{red}{-48} \color{blue}{+48} \color{blue}{-189x} & = & \color{red}{189x} +28 \color{blue}{-189x} \color{blue}{+48} \\\Leftrightarrow & -420x-189x& = & 28+48 \\\Leftrightarrow & \color{red}{-609} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-609} & & \\\Leftrightarrow & x = \frac{-76}{609} & & \\ & V = \left\{ \frac{-76}{609} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{4}{3})& = & -7x+\frac{9}{7} \\\Leftrightarrow & 10x+\frac{20}{3}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{+140} & = & \color{red}{-147x} +27 \\\Leftrightarrow & 210x \color{red}{+140} \color{blue}{-140} \color{blue}{+147x} & = & \color{red}{-147x} +27 \color{blue}{+147x} \color{blue}{-140} \\\Leftrightarrow & 210x+147x& = & 27-140 \\\Leftrightarrow & \color{red}{357} x& = & -113 \\\Leftrightarrow & x = \frac{-113}{357} & & \\ & V = \left\{ \frac{-113}{357} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{4}{7})& = & -9x+\frac{2}{3} \\\Leftrightarrow & 8x-\frac{16}{7}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x- \frac{48}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{-48} & = & \color{red}{-189x} +14 \\\Leftrightarrow & 168x \color{red}{-48} \color{blue}{+48} \color{blue}{+189x} & = & \color{red}{-189x} +14 \color{blue}{+189x} \color{blue}{+48} \\\Leftrightarrow & 168x+189x& = & 14+48 \\\Leftrightarrow & \color{red}{357} x& = & 62 \\\Leftrightarrow & x = \frac{62}{357} & & \\ & V = \left\{ \frac{62}{357} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{3}{2})& = & 7x+\frac{5}{12} \\\Leftrightarrow & -20x-\frac{15}{2}& = & 7x+\frac{5}{12} \\ & & & \text{kgv van noemers 2 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-240}{ \color{blue}{12} }x- \frac{90}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -240x \color{red}{-90} & = & \color{red}{84x} +5 \\\Leftrightarrow & -240x \color{red}{-90} \color{blue}{+90} \color{blue}{-84x} & = & \color{red}{84x} +5 \color{blue}{-84x} \color{blue}{+90} \\\Leftrightarrow & -240x-84x& = & 5+90 \\\Leftrightarrow & \color{red}{-324} x& = & 95 \\\Leftrightarrow & x = \frac{95}{-324} & & \\\Leftrightarrow & x = \frac{-95}{324} & & \\ & V = \left\{ \frac{-95}{324} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{2}{5})& = & -5x+\frac{9}{2} \\\Leftrightarrow & -12x+\frac{6}{5}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{+12} & = & \color{red}{-50x} +45 \\\Leftrightarrow & -120x \color{red}{+12} \color{blue}{-12} \color{blue}{+50x} & = & \color{red}{-50x} +45 \color{blue}{+50x} \color{blue}{-12} \\\Leftrightarrow & -120x+50x& = & 45-12 \\\Leftrightarrow & \color{red}{-70} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-70} & & \\\Leftrightarrow & x = \frac{-33}{70} & & \\ & V = \left\{ \frac{-33}{70} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{3}{11})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -12x+\frac{18}{11}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+126} & = & \color{red}{385x} +110 \\\Leftrightarrow & -924x \color{red}{+126} \color{blue}{-126} \color{blue}{-385x} & = & \color{red}{385x} +110 \color{blue}{-385x} \color{blue}{-126} \\\Leftrightarrow & -924x-385x& = & 110-126 \\\Leftrightarrow & \color{red}{-1309} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-1309} & & \\\Leftrightarrow & x = \frac{16}{1309} & & \\ & V = \left\{ \frac{16}{1309} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{5}{4})& = & -7x+\frac{10}{11} \\\Leftrightarrow & -6x+\frac{15}{4}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-264}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{40}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -264x \color{red}{+165} & = & \color{red}{-308x} +40 \\\Leftrightarrow & -264x \color{red}{+165} \color{blue}{-165} \color{blue}{+308x} & = & \color{red}{-308x} +40 \color{blue}{+308x} \color{blue}{-165} \\\Leftrightarrow & -264x+308x& = & 40-165 \\\Leftrightarrow & \color{red}{44} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{44} & & \\ & V = \left\{ \frac{-125}{44} \right\} & \\\end{align}\)