Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{3}{7})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -25x+\frac{15}{7}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-875}{ \color{blue}{35} }x+ \frac{75}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -875x \color{red}{+75} & = & \color{red}{-175x} +42 \\\Leftrightarrow & -875x \color{red}{+75} \color{blue}{-75} \color{blue}{+175x} & = & \color{red}{-175x} +42 \color{blue}{+175x} \color{blue}{-75} \\\Leftrightarrow & -875x+175x& = & 42-75 \\\Leftrightarrow & \color{red}{-700} x& = & -33 \\\Leftrightarrow & x = \frac{-33}{-700} & & \\\Leftrightarrow & x = \frac{33}{700} & & \\ & V = \left\{ \frac{33}{700} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{2}{9})& = & 5x+\frac{7}{9} \\\Leftrightarrow & -4x-\frac{4}{9}& = & 5x+\frac{7}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-36}{ \color{blue}{9} }x- \frac{4}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -36x \color{red}{-4} & = & \color{red}{45x} +7 \\\Leftrightarrow & -36x \color{red}{-4} \color{blue}{+4} \color{blue}{-45x} & = & \color{red}{45x} +7 \color{blue}{-45x} \color{blue}{+4} \\\Leftrightarrow & -36x-45x& = & 7+4 \\\Leftrightarrow & \color{red}{-81} x& = & 11 \\\Leftrightarrow & x = \frac{11}{-81} & & \\\Leftrightarrow & x = \frac{-11}{81} & & \\ & V = \left\{ \frac{-11}{81} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{2}{7})& = & 5x+\frac{5}{11} \\\Leftrightarrow & -9x+\frac{6}{7}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-693}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -693x \color{red}{+66} & = & \color{red}{385x} +35 \\\Leftrightarrow & -693x \color{red}{+66} \color{blue}{-66} \color{blue}{-385x} & = & \color{red}{385x} +35 \color{blue}{-385x} \color{blue}{-66} \\\Leftrightarrow & -693x-385x& = & 35-66 \\\Leftrightarrow & \color{red}{-1078} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-1078} & & \\\Leftrightarrow & x = \frac{31}{1078} & & \\ & V = \left\{ \frac{31}{1078} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{2}{11})& = & -7x+\frac{9}{8} \\\Leftrightarrow & 10x+\frac{10}{11}& = & -7x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{880}{ \color{blue}{88} }x+ \frac{80}{ \color{blue}{88} })& = & (\frac{-616}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 880x \color{red}{+80} & = & \color{red}{-616x} +99 \\\Leftrightarrow & 880x \color{red}{+80} \color{blue}{-80} \color{blue}{+616x} & = & \color{red}{-616x} +99 \color{blue}{+616x} \color{blue}{-80} \\\Leftrightarrow & 880x+616x& = & 99-80 \\\Leftrightarrow & \color{red}{1496} x& = & 19 \\\Leftrightarrow & x = \frac{19}{1496} & & \\ & V = \left\{ \frac{19}{1496} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{4}{7})& = & 7x+\frac{5}{6} \\\Leftrightarrow & 15x+\frac{20}{7}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{630}{ \color{blue}{42} }x+ \frac{120}{ \color{blue}{42} })& = & (\frac{294}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 630x \color{red}{+120} & = & \color{red}{294x} +35 \\\Leftrightarrow & 630x \color{red}{+120} \color{blue}{-120} \color{blue}{-294x} & = & \color{red}{294x} +35 \color{blue}{-294x} \color{blue}{-120} \\\Leftrightarrow & 630x-294x& = & 35-120 \\\Leftrightarrow & \color{red}{336} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{336} & & \\ & V = \left\{ \frac{-85}{336} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{5}{7})& = & 7x+\frac{3}{4} \\\Leftrightarrow & -20x+\frac{20}{7}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-560}{ \color{blue}{28} }x+ \frac{80}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -560x \color{red}{+80} & = & \color{red}{196x} +21 \\\Leftrightarrow & -560x \color{red}{+80} \color{blue}{-80} \color{blue}{-196x} & = & \color{red}{196x} +21 \color{blue}{-196x} \color{blue}{-80} \\\Leftrightarrow & -560x-196x& = & 21-80 \\\Leftrightarrow & \color{red}{-756} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{-756} & & \\\Leftrightarrow & x = \frac{59}{756} & & \\ & V = \left\{ \frac{59}{756} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{2}{5})& = & 9x+\frac{7}{8} \\\Leftrightarrow & -18x+\frac{12}{5}& = & 9x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-720}{ \color{blue}{40} }x+ \frac{96}{ \color{blue}{40} })& = & (\frac{360}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -720x \color{red}{+96} & = & \color{red}{360x} +35 \\\Leftrightarrow & -720x \color{red}{+96} \color{blue}{-96} \color{blue}{-360x} & = & \color{red}{360x} +35 \color{blue}{-360x} \color{blue}{-96} \\\Leftrightarrow & -720x-360x& = & 35-96 \\\Leftrightarrow & \color{red}{-1080} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{-1080} & & \\\Leftrightarrow & x = \frac{61}{1080} & & \\ & V = \left\{ \frac{61}{1080} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{5}{3})& = & -5x+\frac{3}{4} \\\Leftrightarrow & 4x+\frac{10}{3}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{48}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 48x \color{red}{+40} & = & \color{red}{-60x} +9 \\\Leftrightarrow & 48x \color{red}{+40} \color{blue}{-40} \color{blue}{+60x} & = & \color{red}{-60x} +9 \color{blue}{+60x} \color{blue}{-40} \\\Leftrightarrow & 48x+60x& = & 9-40 \\\Leftrightarrow & \color{red}{108} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{108} & & \\ & V = \left\{ \frac{-31}{108} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{5}{11})& = & 9x+\frac{3}{11} \\\Leftrightarrow & 14x+\frac{35}{11}& = & 9x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{154}{ \color{blue}{11} }x+ \frac{35}{ \color{blue}{11} })& = & (\frac{99}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 154x \color{red}{+35} & = & \color{red}{99x} +3 \\\Leftrightarrow & 154x \color{red}{+35} \color{blue}{-35} \color{blue}{-99x} & = & \color{red}{99x} +3 \color{blue}{-99x} \color{blue}{-35} \\\Leftrightarrow & 154x-99x& = & 3-35 \\\Leftrightarrow & \color{red}{55} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{55} & & \\ & V = \left\{ \frac{-32}{55} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{5}{11})& = & 4x+\frac{10}{11} \\\Leftrightarrow & -35x-\frac{35}{11}& = & 4x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-385}{ \color{blue}{11} }x- \frac{35}{ \color{blue}{11} })& = & (\frac{44}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -385x \color{red}{-35} & = & \color{red}{44x} +10 \\\Leftrightarrow & -385x \color{red}{-35} \color{blue}{+35} \color{blue}{-44x} & = & \color{red}{44x} +10 \color{blue}{-44x} \color{blue}{+35} \\\Leftrightarrow & -385x-44x& = & 10+35 \\\Leftrightarrow & \color{red}{-429} x& = & 45 \\\Leftrightarrow & x = \frac{45}{-429} & & \\\Leftrightarrow & x = \frac{-15}{143} & & \\ & V = \left\{ \frac{-15}{143} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{4}{5})& = & 9x+\frac{3}{2} \\\Leftrightarrow & -8x-\frac{8}{5}& = & 9x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-80}{ \color{blue}{10} }x- \frac{16}{ \color{blue}{10} })& = & (\frac{90}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -80x \color{red}{-16} & = & \color{red}{90x} +15 \\\Leftrightarrow & -80x \color{red}{-16} \color{blue}{+16} \color{blue}{-90x} & = & \color{red}{90x} +15 \color{blue}{-90x} \color{blue}{+16} \\\Leftrightarrow & -80x-90x& = & 15+16 \\\Leftrightarrow & \color{red}{-170} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-170} & & \\\Leftrightarrow & x = \frac{-31}{170} & & \\ & V = \left\{ \frac{-31}{170} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{2}{7})& = & -5x+\frac{3}{5} \\\Leftrightarrow & 12x+\frac{6}{7}& = & -5x+\frac{3}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{21}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+30} & = & \color{red}{-175x} +21 \\\Leftrightarrow & 420x \color{red}{+30} \color{blue}{-30} \color{blue}{+175x} & = & \color{red}{-175x} +21 \color{blue}{+175x} \color{blue}{-30} \\\Leftrightarrow & 420x+175x& = & 21-30 \\\Leftrightarrow & \color{red}{595} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{595} & & \\ & V = \left\{ \frac{-9}{595} \right\} & \\\end{align}\)