Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{2}{7})& = & 3x+\frac{9}{10} \\\Leftrightarrow & 25x+\frac{10}{7}& = & 3x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{1750}{ \color{blue}{70} }x+ \frac{100}{ \color{blue}{70} })& = & (\frac{210}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 1750x \color{red}{+100} & = & \color{red}{210x} +63 \\\Leftrightarrow & 1750x \color{red}{+100} \color{blue}{-100} \color{blue}{-210x} & = & \color{red}{210x} +63 \color{blue}{-210x} \color{blue}{-100} \\\Leftrightarrow & 1750x-210x& = & 63-100 \\\Leftrightarrow & \color{red}{1540} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{1540} & & \\ & V = \left\{ \frac{-37}{1540} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{5}{7})& = & 8x+\frac{10}{7} \\\Leftrightarrow & -18x+\frac{30}{7}& = & 8x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-126}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{56}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -126x \color{red}{+30} & = & \color{red}{56x} +10 \\\Leftrightarrow & -126x \color{red}{+30} \color{blue}{-30} \color{blue}{-56x} & = & \color{red}{56x} +10 \color{blue}{-56x} \color{blue}{-30} \\\Leftrightarrow & -126x-56x& = & 10-30 \\\Leftrightarrow & \color{red}{-182} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-182} & & \\\Leftrightarrow & x = \frac{10}{91} & & \\ & V = \left\{ \frac{10}{91} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{2}{5})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -30x+\frac{12}{5}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-450}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -450x \color{red}{+36} & = & \color{red}{-105x} +40 \\\Leftrightarrow & -450x \color{red}{+36} \color{blue}{-36} \color{blue}{+105x} & = & \color{red}{-105x} +40 \color{blue}{+105x} \color{blue}{-36} \\\Leftrightarrow & -450x+105x& = & 40-36 \\\Leftrightarrow & \color{red}{-345} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-345} & & \\\Leftrightarrow & x = \frac{-4}{345} & & \\ & V = \left\{ \frac{-4}{345} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{3}{7})& = & 9x+\frac{3}{2} \\\Leftrightarrow & -8x-\frac{6}{7}& = & 9x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-112}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{126}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -112x \color{red}{-12} & = & \color{red}{126x} +21 \\\Leftrightarrow & -112x \color{red}{-12} \color{blue}{+12} \color{blue}{-126x} & = & \color{red}{126x} +21 \color{blue}{-126x} \color{blue}{+12} \\\Leftrightarrow & -112x-126x& = & 21+12 \\\Leftrightarrow & \color{red}{-238} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-238} & & \\\Leftrightarrow & x = \frac{-33}{238} & & \\ & V = \left\{ \frac{-33}{238} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{3}{5})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 9x+\frac{9}{5}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{315}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 315x \color{red}{+63} & = & \color{red}{-245x} +50 \\\Leftrightarrow & 315x \color{red}{+63} \color{blue}{-63} \color{blue}{+245x} & = & \color{red}{-245x} +50 \color{blue}{+245x} \color{blue}{-63} \\\Leftrightarrow & 315x+245x& = & 50-63 \\\Leftrightarrow & \color{red}{560} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{560} & & \\ & V = \left\{ \frac{-13}{560} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{5}{4})& = & -5x+\frac{2}{9} \\\Leftrightarrow & 12x-\frac{15}{4}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{432}{ \color{blue}{36} }x- \frac{135}{ \color{blue}{36} })& = & (\frac{-180}{ \color{blue}{36} }x+ \frac{8}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 432x \color{red}{-135} & = & \color{red}{-180x} +8 \\\Leftrightarrow & 432x \color{red}{-135} \color{blue}{+135} \color{blue}{+180x} & = & \color{red}{-180x} +8 \color{blue}{+180x} \color{blue}{+135} \\\Leftrightarrow & 432x+180x& = & 8+135 \\\Leftrightarrow & \color{red}{612} x& = & 143 \\\Leftrightarrow & x = \frac{143}{612} & & \\ & V = \left\{ \frac{143}{612} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{2}{11})& = & 3x+\frac{7}{4} \\\Leftrightarrow & 10x-\frac{10}{11}& = & 3x+\frac{7}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{440}{ \color{blue}{44} }x- \frac{40}{ \color{blue}{44} })& = & (\frac{132}{ \color{blue}{44} }x+ \frac{77}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 440x \color{red}{-40} & = & \color{red}{132x} +77 \\\Leftrightarrow & 440x \color{red}{-40} \color{blue}{+40} \color{blue}{-132x} & = & \color{red}{132x} +77 \color{blue}{-132x} \color{blue}{+40} \\\Leftrightarrow & 440x-132x& = & 77+40 \\\Leftrightarrow & \color{red}{308} x& = & 117 \\\Leftrightarrow & x = \frac{117}{308} & & \\ & V = \left\{ \frac{117}{308} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{2}{3})& = & -4x+\frac{6}{5} \\\Leftrightarrow & 21x+\frac{14}{3}& = & -4x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{315}{ \color{blue}{15} }x+ \frac{70}{ \color{blue}{15} })& = & (\frac{-60}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 315x \color{red}{+70} & = & \color{red}{-60x} +18 \\\Leftrightarrow & 315x \color{red}{+70} \color{blue}{-70} \color{blue}{+60x} & = & \color{red}{-60x} +18 \color{blue}{+60x} \color{blue}{-70} \\\Leftrightarrow & 315x+60x& = & 18-70 \\\Leftrightarrow & \color{red}{375} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{375} & & \\ & V = \left\{ \frac{-52}{375} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{5}{4})& = & -2x+\frac{9}{4} \\\Leftrightarrow & 21x-\frac{35}{4}& = & -2x+\frac{9}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{84}{ \color{blue}{4} }x- \frac{35}{ \color{blue}{4} })& = & (\frac{-8}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 84x \color{red}{-35} & = & \color{red}{-8x} +9 \\\Leftrightarrow & 84x \color{red}{-35} \color{blue}{+35} \color{blue}{+8x} & = & \color{red}{-8x} +9 \color{blue}{+8x} \color{blue}{+35} \\\Leftrightarrow & 84x+8x& = & 9+35 \\\Leftrightarrow & \color{red}{92} x& = & 44 \\\Leftrightarrow & x = \frac{44}{92} & & \\\Leftrightarrow & x = \frac{11}{23} & & \\ & V = \left\{ \frac{11}{23} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{3}{4})& = & -2x+\frac{10}{7} \\\Leftrightarrow & 25x-\frac{15}{4}& = & -2x+\frac{10}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{700}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-56}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 700x \color{red}{-105} & = & \color{red}{-56x} +40 \\\Leftrightarrow & 700x \color{red}{-105} \color{blue}{+105} \color{blue}{+56x} & = & \color{red}{-56x} +40 \color{blue}{+56x} \color{blue}{+105} \\\Leftrightarrow & 700x+56x& = & 40+105 \\\Leftrightarrow & \color{red}{756} x& = & 145 \\\Leftrightarrow & x = \frac{145}{756} & & \\ & V = \left\{ \frac{145}{756} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{3}{2})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -20x+\frac{15}{2}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-280}{ \color{blue}{14} }x+ \frac{105}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -280x \color{red}{+105} & = & \color{red}{-98x} +20 \\\Leftrightarrow & -280x \color{red}{+105} \color{blue}{-105} \color{blue}{+98x} & = & \color{red}{-98x} +20 \color{blue}{+98x} \color{blue}{-105} \\\Leftrightarrow & -280x+98x& = & 20-105 \\\Leftrightarrow & \color{red}{-182} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{-182} & & \\\Leftrightarrow & x = \frac{85}{182} & & \\ & V = \left\{ \frac{85}{182} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{2}{11})& = & 7x+\frac{9}{10} \\\Leftrightarrow & -16x-\frac{8}{11}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1760}{ \color{blue}{110} }x- \frac{80}{ \color{blue}{110} })& = & (\frac{770}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1760x \color{red}{-80} & = & \color{red}{770x} +99 \\\Leftrightarrow & -1760x \color{red}{-80} \color{blue}{+80} \color{blue}{-770x} & = & \color{red}{770x} +99 \color{blue}{-770x} \color{blue}{+80} \\\Leftrightarrow & -1760x-770x& = & 99+80 \\\Leftrightarrow & \color{red}{-2530} x& = & 179 \\\Leftrightarrow & x = \frac{179}{-2530} & & \\\Leftrightarrow & x = \frac{-179}{2530} & & \\ & V = \left\{ \frac{-179}{2530} \right\} & \\\end{align}\)