Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{3}{11})& = & -3x+\frac{4}{7} \\\Leftrightarrow & 10x-\frac{6}{11}& = & -3x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x- \frac{42}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{-42} & = & \color{red}{-231x} +44 \\\Leftrightarrow & 770x \color{red}{-42} \color{blue}{+42} \color{blue}{+231x} & = & \color{red}{-231x} +44 \color{blue}{+231x} \color{blue}{+42} \\\Leftrightarrow & 770x+231x& = & 44+42 \\\Leftrightarrow & \color{red}{1001} x& = & 86 \\\Leftrightarrow & x = \frac{86}{1001} & & \\ & V = \left\{ \frac{86}{1001} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+1)& = & 3x+\frac{7}{10} \\\Leftrightarrow & -20x-5& = & 3x+\frac{7}{10} \\ & & & \text{kgv van noemers 1 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-200}{ \color{blue}{10} }x- \frac{50}{ \color{blue}{10} })& = & (\frac{30}{ \color{blue}{10} }x+ \frac{7}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -200x \color{red}{-50} & = & \color{red}{30x} +7 \\\Leftrightarrow & -200x \color{red}{-50} \color{blue}{+50} \color{blue}{-30x} & = & \color{red}{30x} +7 \color{blue}{-30x} \color{blue}{+50} \\\Leftrightarrow & -200x-30x& = & 7+50 \\\Leftrightarrow & \color{red}{-230} x& = & 57 \\\Leftrightarrow & x = \frac{57}{-230} & & \\\Leftrightarrow & x = \frac{-57}{230} & & \\ & V = \left\{ \frac{-57}{230} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{7})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -6x+\frac{10}{7}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{+30} & = & \color{red}{-147x} +28 \\\Leftrightarrow & -126x \color{red}{+30} \color{blue}{-30} \color{blue}{+147x} & = & \color{red}{-147x} +28 \color{blue}{+147x} \color{blue}{-30} \\\Leftrightarrow & -126x+147x& = & 28-30 \\\Leftrightarrow & \color{red}{21} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{21} & & \\ & V = \left\{ \frac{-2}{21} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{5}{4})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 6x-\frac{15}{4}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{264}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{24}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 264x \color{red}{-165} & = & \color{red}{-308x} +24 \\\Leftrightarrow & 264x \color{red}{-165} \color{blue}{+165} \color{blue}{+308x} & = & \color{red}{-308x} +24 \color{blue}{+308x} \color{blue}{+165} \\\Leftrightarrow & 264x+308x& = & 24+165 \\\Leftrightarrow & \color{red}{572} x& = & 189 \\\Leftrightarrow & x = \frac{189}{572} & & \\ & V = \left\{ \frac{189}{572} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{2}{5})& = & 5x+\frac{7}{11} \\\Leftrightarrow & 18x+\frac{12}{5}& = & 5x+\frac{7}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{35}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{+132} & = & \color{red}{275x} +35 \\\Leftrightarrow & 990x \color{red}{+132} \color{blue}{-132} \color{blue}{-275x} & = & \color{red}{275x} +35 \color{blue}{-275x} \color{blue}{-132} \\\Leftrightarrow & 990x-275x& = & 35-132 \\\Leftrightarrow & \color{red}{715} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{715} & & \\ & V = \left\{ \frac{-97}{715} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{4}{9})& = & 3x+\frac{2}{7} \\\Leftrightarrow & 8x-\frac{8}{9}& = & 3x+\frac{2}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x- \frac{56}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{18}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{-56} & = & \color{red}{189x} +18 \\\Leftrightarrow & 504x \color{red}{-56} \color{blue}{+56} \color{blue}{-189x} & = & \color{red}{189x} +18 \color{blue}{-189x} \color{blue}{+56} \\\Leftrightarrow & 504x-189x& = & 18+56 \\\Leftrightarrow & \color{red}{315} x& = & 74 \\\Leftrightarrow & x = \frac{74}{315} & & \\ & V = \left\{ \frac{74}{315} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{3}{8})& = & 9x+\frac{2}{5} \\\Leftrightarrow & 14x-\frac{21}{8}& = & 9x+\frac{2}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{560}{ \color{blue}{40} }x- \frac{105}{ \color{blue}{40} })& = & (\frac{360}{ \color{blue}{40} }x+ \frac{16}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 560x \color{red}{-105} & = & \color{red}{360x} +16 \\\Leftrightarrow & 560x \color{red}{-105} \color{blue}{+105} \color{blue}{-360x} & = & \color{red}{360x} +16 \color{blue}{-360x} \color{blue}{+105} \\\Leftrightarrow & 560x-360x& = & 16+105 \\\Leftrightarrow & \color{red}{200} x& = & 121 \\\Leftrightarrow & x = \frac{121}{200} & & \\ & V = \left\{ \frac{121}{200} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{5}{9})& = & -9x+\frac{9}{2} \\\Leftrightarrow & 8x-\frac{20}{9}& = & -9x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{144}{ \color{blue}{18} }x- \frac{40}{ \color{blue}{18} })& = & (\frac{-162}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 144x \color{red}{-40} & = & \color{red}{-162x} +81 \\\Leftrightarrow & 144x \color{red}{-40} \color{blue}{+40} \color{blue}{+162x} & = & \color{red}{-162x} +81 \color{blue}{+162x} \color{blue}{+40} \\\Leftrightarrow & 144x+162x& = & 81+40 \\\Leftrightarrow & \color{red}{306} x& = & 121 \\\Leftrightarrow & x = \frac{121}{306} & & \\ & V = \left\{ \frac{121}{306} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{2}{7})& = & -7x+\frac{3}{7} \\\Leftrightarrow & -20x-\frac{10}{7}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-140}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -140x \color{red}{-10} & = & \color{red}{-49x} +3 \\\Leftrightarrow & -140x \color{red}{-10} \color{blue}{+10} \color{blue}{+49x} & = & \color{red}{-49x} +3 \color{blue}{+49x} \color{blue}{+10} \\\Leftrightarrow & -140x+49x& = & 3+10 \\\Leftrightarrow & \color{red}{-91} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-91} & & \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{3}{8})& = & 9x+\frac{3}{7} \\\Leftrightarrow & 28x+\frac{21}{8}& = & 9x+\frac{3}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1568}{ \color{blue}{56} }x+ \frac{147}{ \color{blue}{56} })& = & (\frac{504}{ \color{blue}{56} }x+ \frac{24}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1568x \color{red}{+147} & = & \color{red}{504x} +24 \\\Leftrightarrow & 1568x \color{red}{+147} \color{blue}{-147} \color{blue}{-504x} & = & \color{red}{504x} +24 \color{blue}{-504x} \color{blue}{-147} \\\Leftrightarrow & 1568x-504x& = & 24-147 \\\Leftrightarrow & \color{red}{1064} x& = & -123 \\\Leftrightarrow & x = \frac{-123}{1064} & & \\ & V = \left\{ \frac{-123}{1064} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{5}{7})& = & -7x+\frac{5}{12} \\\Leftrightarrow & -6x-\frac{15}{7}& = & -7x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-504}{ \color{blue}{84} }x- \frac{180}{ \color{blue}{84} })& = & (\frac{-588}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -504x \color{red}{-180} & = & \color{red}{-588x} +35 \\\Leftrightarrow & -504x \color{red}{-180} \color{blue}{+180} \color{blue}{+588x} & = & \color{red}{-588x} +35 \color{blue}{+588x} \color{blue}{+180} \\\Leftrightarrow & -504x+588x& = & 35+180 \\\Leftrightarrow & \color{red}{84} x& = & 215 \\\Leftrightarrow & x = \frac{215}{84} & & \\ & V = \left\{ \frac{215}{84} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{3}{11})& = & 5x+\frac{6}{7} \\\Leftrightarrow & -24x+\frac{18}{11}& = & 5x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{+126} & = & \color{red}{385x} +66 \\\Leftrightarrow & -1848x \color{red}{+126} \color{blue}{-126} \color{blue}{-385x} & = & \color{red}{385x} +66 \color{blue}{-385x} \color{blue}{-126} \\\Leftrightarrow & -1848x-385x& = & 66-126 \\\Leftrightarrow & \color{red}{-2233} x& = & -60 \\\Leftrightarrow & x = \frac{-60}{-2233} & & \\\Leftrightarrow & x = \frac{60}{2233} & & \\ & V = \left\{ \frac{60}{2233} \right\} & \\\end{align}\)