Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{5}{7})& = & 9x+\frac{4}{3} \\\Leftrightarrow & 20x+\frac{25}{7}& = & 9x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x+ \frac{75}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{+75} & = & \color{red}{189x} +28 \\\Leftrightarrow & 420x \color{red}{+75} \color{blue}{-75} \color{blue}{-189x} & = & \color{red}{189x} +28 \color{blue}{-189x} \color{blue}{-75} \\\Leftrightarrow & 420x-189x& = & 28-75 \\\Leftrightarrow & \color{red}{231} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{231} & & \\ & V = \left\{ \frac{-47}{231} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{3}{11})& = & -5x+\frac{10}{11} \\\Leftrightarrow & -9x+\frac{9}{11}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-99}{ \color{blue}{11} }x+ \frac{9}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -99x \color{red}{+9} & = & \color{red}{-55x} +10 \\\Leftrightarrow & -99x \color{red}{+9} \color{blue}{-9} \color{blue}{+55x} & = & \color{red}{-55x} +10 \color{blue}{+55x} \color{blue}{-9} \\\Leftrightarrow & -99x+55x& = & 10-9 \\\Leftrightarrow & \color{red}{-44} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-44} & & \\\Leftrightarrow & x = \frac{-1}{44} & & \\ & V = \left\{ \frac{-1}{44} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{5}{6})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 35x-\frac{35}{6}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{1050}{ \color{blue}{30} }x- \frac{175}{ \color{blue}{30} })& = & (\frac{-90}{ \color{blue}{30} }x+ \frac{36}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 1050x \color{red}{-175} & = & \color{red}{-90x} +36 \\\Leftrightarrow & 1050x \color{red}{-175} \color{blue}{+175} \color{blue}{+90x} & = & \color{red}{-90x} +36 \color{blue}{+90x} \color{blue}{+175} \\\Leftrightarrow & 1050x+90x& = & 36+175 \\\Leftrightarrow & \color{red}{1140} x& = & 211 \\\Leftrightarrow & x = \frac{211}{1140} & & \\ & V = \left\{ \frac{211}{1140} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{5}{7})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -12x+\frac{30}{7}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{+30} & = & \color{red}{35x} +10 \\\Leftrightarrow & -84x \color{red}{+30} \color{blue}{-30} \color{blue}{-35x} & = & \color{red}{35x} +10 \color{blue}{-35x} \color{blue}{-30} \\\Leftrightarrow & -84x-35x& = & 10-30 \\\Leftrightarrow & \color{red}{-119} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-119} & & \\\Leftrightarrow & x = \frac{20}{119} & & \\ & V = \left\{ \frac{20}{119} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{2}{3})& = & -8x+\frac{8}{3} \\\Leftrightarrow & -21x-\frac{14}{3}& = & -8x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-63}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{-24}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -63x \color{red}{-14} & = & \color{red}{-24x} +8 \\\Leftrightarrow & -63x \color{red}{-14} \color{blue}{+14} \color{blue}{+24x} & = & \color{red}{-24x} +8 \color{blue}{+24x} \color{blue}{+14} \\\Leftrightarrow & -63x+24x& = & 8+14 \\\Leftrightarrow & \color{red}{-39} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-39} & & \\\Leftrightarrow & x = \frac{-22}{39} & & \\ & V = \left\{ \frac{-22}{39} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{3}{7})& = & 5x+\frac{3}{4} \\\Leftrightarrow & 6x+\frac{6}{7}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{168}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 168x \color{red}{+24} & = & \color{red}{140x} +21 \\\Leftrightarrow & 168x \color{red}{+24} \color{blue}{-24} \color{blue}{-140x} & = & \color{red}{140x} +21 \color{blue}{-140x} \color{blue}{-24} \\\Leftrightarrow & 168x-140x& = & 21-24 \\\Leftrightarrow & \color{red}{28} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{28} & & \\ & V = \left\{ \frac{-3}{28} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{3}{5})& = & 7x+\frac{3}{7} \\\Leftrightarrow & 8x-\frac{12}{5}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{-84} & = & \color{red}{245x} +15 \\\Leftrightarrow & 280x \color{red}{-84} \color{blue}{+84} \color{blue}{-245x} & = & \color{red}{245x} +15 \color{blue}{-245x} \color{blue}{+84} \\\Leftrightarrow & 280x-245x& = & 15+84 \\\Leftrightarrow & \color{red}{35} x& = & 99 \\\Leftrightarrow & x = \frac{99}{35} & & \\ & V = \left\{ \frac{99}{35} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{2}{7})& = & 4x+\frac{6}{11} \\\Leftrightarrow & -15x-\frac{10}{7}& = & 4x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{308}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{-110} & = & \color{red}{308x} +42 \\\Leftrightarrow & -1155x \color{red}{-110} \color{blue}{+110} \color{blue}{-308x} & = & \color{red}{308x} +42 \color{blue}{-308x} \color{blue}{+110} \\\Leftrightarrow & -1155x-308x& = & 42+110 \\\Leftrightarrow & \color{red}{-1463} x& = & 152 \\\Leftrightarrow & x = \frac{152}{-1463} & & \\\Leftrightarrow & x = \frac{-8}{77} & & \\ & V = \left\{ \frac{-8}{77} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{5}{4})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -9x-\frac{15}{4}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-108}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -108x \color{red}{-45} & = & \color{red}{-84x} +8 \\\Leftrightarrow & -108x \color{red}{-45} \color{blue}{+45} \color{blue}{+84x} & = & \color{red}{-84x} +8 \color{blue}{+84x} \color{blue}{+45} \\\Leftrightarrow & -108x+84x& = & 8+45 \\\Leftrightarrow & \color{red}{-24} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-24} & & \\\Leftrightarrow & x = \frac{-53}{24} & & \\ & V = \left\{ \frac{-53}{24} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{4}{3})& = & -4x+\frac{4}{7} \\\Leftrightarrow & -15x-\frac{20}{3}& = & -4x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{-84}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{-140} & = & \color{red}{-84x} +12 \\\Leftrightarrow & -315x \color{red}{-140} \color{blue}{+140} \color{blue}{+84x} & = & \color{red}{-84x} +12 \color{blue}{+84x} \color{blue}{+140} \\\Leftrightarrow & -315x+84x& = & 12+140 \\\Leftrightarrow & \color{red}{-231} x& = & 152 \\\Leftrightarrow & x = \frac{152}{-231} & & \\\Leftrightarrow & x = \frac{-152}{231} & & \\ & V = \left\{ \frac{-152}{231} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{3}{7})& = & 7x+\frac{10}{9} \\\Leftrightarrow & -6x+\frac{6}{7}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-378}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -378x \color{red}{+54} & = & \color{red}{441x} +70 \\\Leftrightarrow & -378x \color{red}{+54} \color{blue}{-54} \color{blue}{-441x} & = & \color{red}{441x} +70 \color{blue}{-441x} \color{blue}{-54} \\\Leftrightarrow & -378x-441x& = & 70-54 \\\Leftrightarrow & \color{red}{-819} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-819} & & \\\Leftrightarrow & x = \frac{-16}{819} & & \\ & V = \left\{ \frac{-16}{819} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{2}{11})& = & -7x+\frac{4}{7} \\\Leftrightarrow & -30x+\frac{12}{11}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x+ \frac{84}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{+84} & = & \color{red}{-539x} +44 \\\Leftrightarrow & -2310x \color{red}{+84} \color{blue}{-84} \color{blue}{+539x} & = & \color{red}{-539x} +44 \color{blue}{+539x} \color{blue}{-84} \\\Leftrightarrow & -2310x+539x& = & 44-84 \\\Leftrightarrow & \color{red}{-1771} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{-1771} & & \\\Leftrightarrow & x = \frac{40}{1771} & & \\ & V = \left\{ \frac{40}{1771} \right\} & \\\end{align}\)