Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{4}{7})& = & -3x+\frac{5}{6} \\\Leftrightarrow & -8x-\frac{16}{7}& = & -3x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-336}{ \color{blue}{42} }x- \frac{96}{ \color{blue}{42} })& = & (\frac{-126}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -336x \color{red}{-96} & = & \color{red}{-126x} +35 \\\Leftrightarrow & -336x \color{red}{-96} \color{blue}{+96} \color{blue}{+126x} & = & \color{red}{-126x} +35 \color{blue}{+126x} \color{blue}{+96} \\\Leftrightarrow & -336x+126x& = & 35+96 \\\Leftrightarrow & \color{red}{-210} x& = & 131 \\\Leftrightarrow & x = \frac{131}{-210} & & \\\Leftrightarrow & x = \frac{-131}{210} & & \\ & V = \left\{ \frac{-131}{210} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{5}{2})& = & -8x+\frac{9}{7} \\\Leftrightarrow & 15x-\frac{25}{2}& = & -8x+\frac{9}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{210}{ \color{blue}{14} }x- \frac{175}{ \color{blue}{14} })& = & (\frac{-112}{ \color{blue}{14} }x+ \frac{18}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 210x \color{red}{-175} & = & \color{red}{-112x} +18 \\\Leftrightarrow & 210x \color{red}{-175} \color{blue}{+175} \color{blue}{+112x} & = & \color{red}{-112x} +18 \color{blue}{+112x} \color{blue}{+175} \\\Leftrightarrow & 210x+112x& = & 18+175 \\\Leftrightarrow & \color{red}{322} x& = & 193 \\\Leftrightarrow & x = \frac{193}{322} & & \\ & V = \left\{ \frac{193}{322} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{2}{3})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 12x+\frac{8}{3}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{36}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 36x \color{red}{+8} & = & \color{red}{-15x} +8 \\\Leftrightarrow & 36x \color{red}{+8} \color{blue}{-8} \color{blue}{+15x} & = & \color{red}{-15x} +8 \color{blue}{+15x} \color{blue}{-8} \\\Leftrightarrow & 36x+15x& = & 8-8 \\\Leftrightarrow & \color{red}{51} x& = & 0 \\\Leftrightarrow & x = \frac{0}{51} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{2}{5})& = & -5x+\frac{3}{10} \\\Leftrightarrow & -24x+\frac{12}{5}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-240}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -240x \color{red}{+24} & = & \color{red}{-50x} +3 \\\Leftrightarrow & -240x \color{red}{+24} \color{blue}{-24} \color{blue}{+50x} & = & \color{red}{-50x} +3 \color{blue}{+50x} \color{blue}{-24} \\\Leftrightarrow & -240x+50x& = & 3-24 \\\Leftrightarrow & \color{red}{-190} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{-190} & & \\\Leftrightarrow & x = \frac{21}{190} & & \\ & V = \left\{ \frac{21}{190} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{2}{3})& = & -7x+\frac{9}{4} \\\Leftrightarrow & 8x+\frac{8}{3}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{96}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 96x \color{red}{+32} & = & \color{red}{-84x} +27 \\\Leftrightarrow & 96x \color{red}{+32} \color{blue}{-32} \color{blue}{+84x} & = & \color{red}{-84x} +27 \color{blue}{+84x} \color{blue}{-32} \\\Leftrightarrow & 96x+84x& = & 27-32 \\\Leftrightarrow & \color{red}{180} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{180} & & \\\Leftrightarrow & x = \frac{-1}{36} & & \\ & V = \left\{ \frac{-1}{36} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{5}{12})& = & -4x+\frac{7}{2} \\\Leftrightarrow & 15x-\frac{25}{12}& = & -4x+\frac{7}{2} \\ & & & \text{kgv van noemers 12 en 2 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x- \frac{25}{ \color{blue}{12} })& = & (\frac{-48}{ \color{blue}{12} }x+ \frac{42}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{-25} & = & \color{red}{-48x} +42 \\\Leftrightarrow & 180x \color{red}{-25} \color{blue}{+25} \color{blue}{+48x} & = & \color{red}{-48x} +42 \color{blue}{+48x} \color{blue}{+25} \\\Leftrightarrow & 180x+48x& = & 42+25 \\\Leftrightarrow & \color{red}{228} x& = & 67 \\\Leftrightarrow & x = \frac{67}{228} & & \\ & V = \left\{ \frac{67}{228} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{5}{11})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -30x+\frac{30}{11}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x+ \frac{210}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{+210} & = & \color{red}{539x} +99 \\\Leftrightarrow & -2310x \color{red}{+210} \color{blue}{-210} \color{blue}{-539x} & = & \color{red}{539x} +99 \color{blue}{-539x} \color{blue}{-210} \\\Leftrightarrow & -2310x-539x& = & 99-210 \\\Leftrightarrow & \color{red}{-2849} x& = & -111 \\\Leftrightarrow & x = \frac{-111}{-2849} & & \\\Leftrightarrow & x = \frac{3}{77} & & \\ & V = \left\{ \frac{3}{77} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{4}{9})& = & -3x+\frac{5}{2} \\\Leftrightarrow & -20x+\frac{20}{9}& = & -3x+\frac{5}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-360}{ \color{blue}{18} }x+ \frac{40}{ \color{blue}{18} })& = & (\frac{-54}{ \color{blue}{18} }x+ \frac{45}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -360x \color{red}{+40} & = & \color{red}{-54x} +45 \\\Leftrightarrow & -360x \color{red}{+40} \color{blue}{-40} \color{blue}{+54x} & = & \color{red}{-54x} +45 \color{blue}{+54x} \color{blue}{-40} \\\Leftrightarrow & -360x+54x& = & 45-40 \\\Leftrightarrow & \color{red}{-306} x& = & 5 \\\Leftrightarrow & x = \frac{5}{-306} & & \\\Leftrightarrow & x = \frac{-5}{306} & & \\ & V = \left\{ \frac{-5}{306} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{3}{10})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 6x+\frac{9}{10}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{180}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} })& = & (\frac{-150}{ \color{blue}{30} }x+ \frac{80}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 180x \color{red}{+27} & = & \color{red}{-150x} +80 \\\Leftrightarrow & 180x \color{red}{+27} \color{blue}{-27} \color{blue}{+150x} & = & \color{red}{-150x} +80 \color{blue}{+150x} \color{blue}{-27} \\\Leftrightarrow & 180x+150x& = & 80-27 \\\Leftrightarrow & \color{red}{330} x& = & 53 \\\Leftrightarrow & x = \frac{53}{330} & & \\ & V = \left\{ \frac{53}{330} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{4}{7})& = & -7x+\frac{2}{5} \\\Leftrightarrow & 8x+\frac{16}{7}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x+ \frac{80}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{+80} & = & \color{red}{-245x} +14 \\\Leftrightarrow & 280x \color{red}{+80} \color{blue}{-80} \color{blue}{+245x} & = & \color{red}{-245x} +14 \color{blue}{+245x} \color{blue}{-80} \\\Leftrightarrow & 280x+245x& = & 14-80 \\\Leftrightarrow & \color{red}{525} x& = & -66 \\\Leftrightarrow & x = \frac{-66}{525} & & \\\Leftrightarrow & x = \frac{-22}{175} & & \\ & V = \left\{ \frac{-22}{175} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{3}{7})& = & 9x+\frac{8}{3} \\\Leftrightarrow & 8x+\frac{6}{7}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{+18} & = & \color{red}{189x} +56 \\\Leftrightarrow & 168x \color{red}{+18} \color{blue}{-18} \color{blue}{-189x} & = & \color{red}{189x} +56 \color{blue}{-189x} \color{blue}{-18} \\\Leftrightarrow & 168x-189x& = & 56-18 \\\Leftrightarrow & \color{red}{-21} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-21} & & \\\Leftrightarrow & x = \frac{-38}{21} & & \\ & V = \left\{ \frac{-38}{21} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{2}{5})& = & -3x+\frac{10}{7} \\\Leftrightarrow & -14x+\frac{14}{5}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-490}{ \color{blue}{35} }x+ \frac{98}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -490x \color{red}{+98} & = & \color{red}{-105x} +50 \\\Leftrightarrow & -490x \color{red}{+98} \color{blue}{-98} \color{blue}{+105x} & = & \color{red}{-105x} +50 \color{blue}{+105x} \color{blue}{-98} \\\Leftrightarrow & -490x+105x& = & 50-98 \\\Leftrightarrow & \color{red}{-385} x& = & -48 \\\Leftrightarrow & x = \frac{-48}{-385} & & \\\Leftrightarrow & x = \frac{48}{385} & & \\ & V = \left\{ \frac{48}{385} \right\} & \\\end{align}\)