Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{2}{3})& = & 3x+\frac{9}{2} \\\Leftrightarrow & 25x+\frac{10}{3}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{150}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 150x \color{red}{+20} & = & \color{red}{18x} +27 \\\Leftrightarrow & 150x \color{red}{+20} \color{blue}{-20} \color{blue}{-18x} & = & \color{red}{18x} +27 \color{blue}{-18x} \color{blue}{-20} \\\Leftrightarrow & 150x-18x& = & 27-20 \\\Leftrightarrow & \color{red}{132} x& = & 7 \\\Leftrightarrow & x = \frac{7}{132} & & \\ & V = \left\{ \frac{7}{132} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{2}{9})& = & 7x+\frac{7}{6} \\\Leftrightarrow & 20x+\frac{8}{9}& = & 7x+\frac{7}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{360}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{21}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 360x \color{red}{+16} & = & \color{red}{126x} +21 \\\Leftrightarrow & 360x \color{red}{+16} \color{blue}{-16} \color{blue}{-126x} & = & \color{red}{126x} +21 \color{blue}{-126x} \color{blue}{-16} \\\Leftrightarrow & 360x-126x& = & 21-16 \\\Leftrightarrow & \color{red}{234} x& = & 5 \\\Leftrightarrow & x = \frac{5}{234} & & \\ & V = \left\{ \frac{5}{234} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{5}{2})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 12x-\frac{15}{2}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x- \frac{105}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{-105} & = & \color{red}{-70x} +12 \\\Leftrightarrow & 168x \color{red}{-105} \color{blue}{+105} \color{blue}{+70x} & = & \color{red}{-70x} +12 \color{blue}{+70x} \color{blue}{+105} \\\Leftrightarrow & 168x+70x& = & 12+105 \\\Leftrightarrow & \color{red}{238} x& = & 117 \\\Leftrightarrow & x = \frac{117}{238} & & \\ & V = \left\{ \frac{117}{238} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{2}{11})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 4x+\frac{4}{11}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{88}{ \color{blue}{22} }x+ \frac{8}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 88x \color{red}{+8} & = & \color{red}{-110x} +33 \\\Leftrightarrow & 88x \color{red}{+8} \color{blue}{-8} \color{blue}{+110x} & = & \color{red}{-110x} +33 \color{blue}{+110x} \color{blue}{-8} \\\Leftrightarrow & 88x+110x& = & 33-8 \\\Leftrightarrow & \color{red}{198} x& = & 25 \\\Leftrightarrow & x = \frac{25}{198} & & \\ & V = \left\{ \frac{25}{198} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{5}{12})& = & -2x+\frac{3}{7} \\\Leftrightarrow & 25x+\frac{25}{12}& = & -2x+\frac{3}{7} \\ & & & \text{kgv van noemers 12 en 7 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{2100}{ \color{blue}{84} }x+ \frac{175}{ \color{blue}{84} })& = & (\frac{-168}{ \color{blue}{84} }x+ \frac{36}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 2100x \color{red}{+175} & = & \color{red}{-168x} +36 \\\Leftrightarrow & 2100x \color{red}{+175} \color{blue}{-175} \color{blue}{+168x} & = & \color{red}{-168x} +36 \color{blue}{+168x} \color{blue}{-175} \\\Leftrightarrow & 2100x+168x& = & 36-175 \\\Leftrightarrow & \color{red}{2268} x& = & -139 \\\Leftrightarrow & x = \frac{-139}{2268} & & \\ & V = \left\{ \frac{-139}{2268} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{4}{7})& = & -3x+\frac{2}{9} \\\Leftrightarrow & -8x+\frac{16}{7}& = & -3x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-504}{ \color{blue}{63} }x+ \frac{144}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -504x \color{red}{+144} & = & \color{red}{-189x} +14 \\\Leftrightarrow & -504x \color{red}{+144} \color{blue}{-144} \color{blue}{+189x} & = & \color{red}{-189x} +14 \color{blue}{+189x} \color{blue}{-144} \\\Leftrightarrow & -504x+189x& = & 14-144 \\\Leftrightarrow & \color{red}{-315} x& = & -130 \\\Leftrightarrow & x = \frac{-130}{-315} & & \\\Leftrightarrow & x = \frac{26}{63} & & \\ & V = \left\{ \frac{26}{63} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{3}{11})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 30x+\frac{18}{11}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2310}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2310x \color{red}{+126} & = & \color{red}{539x} +110 \\\Leftrightarrow & 2310x \color{red}{+126} \color{blue}{-126} \color{blue}{-539x} & = & \color{red}{539x} +110 \color{blue}{-539x} \color{blue}{-126} \\\Leftrightarrow & 2310x-539x& = & 110-126 \\\Leftrightarrow & \color{red}{1771} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{1771} & & \\ & V = \left\{ \frac{-16}{1771} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{4}{5})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-84} & = & \color{red}{-175x} +30 \\\Leftrightarrow & 420x \color{red}{-84} \color{blue}{+84} \color{blue}{+175x} & = & \color{red}{-175x} +30 \color{blue}{+175x} \color{blue}{+84} \\\Leftrightarrow & 420x+175x& = & 30+84 \\\Leftrightarrow & \color{red}{595} x& = & 114 \\\Leftrightarrow & x = \frac{114}{595} & & \\ & V = \left\{ \frac{114}{595} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{4}{5})& = & -9x+\frac{2}{3} \\\Leftrightarrow & 14x-\frac{28}{5}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{210}{ \color{blue}{15} }x- \frac{84}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 210x \color{red}{-84} & = & \color{red}{-135x} +10 \\\Leftrightarrow & 210x \color{red}{-84} \color{blue}{+84} \color{blue}{+135x} & = & \color{red}{-135x} +10 \color{blue}{+135x} \color{blue}{+84} \\\Leftrightarrow & 210x+135x& = & 10+84 \\\Leftrightarrow & \color{red}{345} x& = & 94 \\\Leftrightarrow & x = \frac{94}{345} & & \\ & V = \left\{ \frac{94}{345} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{5}{8})& = & 2x+\frac{6}{5} \\\Leftrightarrow & 15x+\frac{15}{8}& = & 2x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{600}{ \color{blue}{40} }x+ \frac{75}{ \color{blue}{40} })& = & (\frac{80}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 600x \color{red}{+75} & = & \color{red}{80x} +48 \\\Leftrightarrow & 600x \color{red}{+75} \color{blue}{-75} \color{blue}{-80x} & = & \color{red}{80x} +48 \color{blue}{-80x} \color{blue}{-75} \\\Leftrightarrow & 600x-80x& = & 48-75 \\\Leftrightarrow & \color{red}{520} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{520} & & \\ & V = \left\{ \frac{-27}{520} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{3}{11})& = & 9x+\frac{9}{4} \\\Leftrightarrow & -20x-\frac{15}{11}& = & 9x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-880}{ \color{blue}{44} }x- \frac{60}{ \color{blue}{44} })& = & (\frac{396}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -880x \color{red}{-60} & = & \color{red}{396x} +99 \\\Leftrightarrow & -880x \color{red}{-60} \color{blue}{+60} \color{blue}{-396x} & = & \color{red}{396x} +99 \color{blue}{-396x} \color{blue}{+60} \\\Leftrightarrow & -880x-396x& = & 99+60 \\\Leftrightarrow & \color{red}{-1276} x& = & 159 \\\Leftrightarrow & x = \frac{159}{-1276} & & \\\Leftrightarrow & x = \frac{-159}{1276} & & \\ & V = \left\{ \frac{-159}{1276} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{5}{3})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 12x+\frac{20}{3}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+100} & = & \color{red}{105x} +18 \\\Leftrightarrow & 180x \color{red}{+100} \color{blue}{-100} \color{blue}{-105x} & = & \color{red}{105x} +18 \color{blue}{-105x} \color{blue}{-100} \\\Leftrightarrow & 180x-105x& = & 18-100 \\\Leftrightarrow & \color{red}{75} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{75} & & \\ & V = \left\{ \frac{-82}{75} \right\} & \\\end{align}\)