Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{2}{3})& = & -3x+\frac{9}{4} \\\Leftrightarrow & -14x+\frac{14}{3}& = & -3x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-168}{ \color{blue}{12} }x+ \frac{56}{ \color{blue}{12} })& = & (\frac{-36}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -168x \color{red}{+56} & = & \color{red}{-36x} +27 \\\Leftrightarrow & -168x \color{red}{+56} \color{blue}{-56} \color{blue}{+36x} & = & \color{red}{-36x} +27 \color{blue}{+36x} \color{blue}{-56} \\\Leftrightarrow & -168x+36x& = & 27-56 \\\Leftrightarrow & \color{red}{-132} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-132} & & \\\Leftrightarrow & x = \frac{29}{132} & & \\ & V = \left\{ \frac{29}{132} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{4}{7})& = & 3x+\frac{2}{3} \\\Leftrightarrow & 16x-\frac{16}{7}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x- \frac{48}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{-48} & = & \color{red}{63x} +14 \\\Leftrightarrow & 336x \color{red}{-48} \color{blue}{+48} \color{blue}{-63x} & = & \color{red}{63x} +14 \color{blue}{-63x} \color{blue}{+48} \\\Leftrightarrow & 336x-63x& = & 14+48 \\\Leftrightarrow & \color{red}{273} x& = & 62 \\\Leftrightarrow & x = \frac{62}{273} & & \\ & V = \left\{ \frac{62}{273} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{5}{7})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 12x-\frac{30}{7}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{-90} & = & \color{red}{-147x} +14 \\\Leftrightarrow & 252x \color{red}{-90} \color{blue}{+90} \color{blue}{+147x} & = & \color{red}{-147x} +14 \color{blue}{+147x} \color{blue}{+90} \\\Leftrightarrow & 252x+147x& = & 14+90 \\\Leftrightarrow & \color{red}{399} x& = & 104 \\\Leftrightarrow & x = \frac{104}{399} & & \\ & V = \left\{ \frac{104}{399} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{2}{3})& = & -2x+\frac{6}{5} \\\Leftrightarrow & 21x-\frac{14}{3}& = & -2x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{315}{ \color{blue}{15} }x- \frac{70}{ \color{blue}{15} })& = & (\frac{-30}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 315x \color{red}{-70} & = & \color{red}{-30x} +18 \\\Leftrightarrow & 315x \color{red}{-70} \color{blue}{+70} \color{blue}{+30x} & = & \color{red}{-30x} +18 \color{blue}{+30x} \color{blue}{+70} \\\Leftrightarrow & 315x+30x& = & 18+70 \\\Leftrightarrow & \color{red}{345} x& = & 88 \\\Leftrightarrow & x = \frac{88}{345} & & \\ & V = \left\{ \frac{88}{345} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{3}{11})& = & -3x+\frac{2}{3} \\\Leftrightarrow & -18x-\frac{18}{11}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-594}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -594x \color{red}{-54} & = & \color{red}{-99x} +22 \\\Leftrightarrow & -594x \color{red}{-54} \color{blue}{+54} \color{blue}{+99x} & = & \color{red}{-99x} +22 \color{blue}{+99x} \color{blue}{+54} \\\Leftrightarrow & -594x+99x& = & 22+54 \\\Leftrightarrow & \color{red}{-495} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-495} & & \\\Leftrightarrow & x = \frac{-76}{495} & & \\ & V = \left\{ \frac{-76}{495} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{3}{11})& = & 5x+\frac{7}{5} \\\Leftrightarrow & -12x+\frac{18}{11}& = & 5x+\frac{7}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{90}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{77}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+90} & = & \color{red}{275x} +77 \\\Leftrightarrow & -660x \color{red}{+90} \color{blue}{-90} \color{blue}{-275x} & = & \color{red}{275x} +77 \color{blue}{-275x} \color{blue}{-90} \\\Leftrightarrow & -660x-275x& = & 77-90 \\\Leftrightarrow & \color{red}{-935} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-935} & & \\\Leftrightarrow & x = \frac{13}{935} & & \\ & V = \left\{ \frac{13}{935} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{3}{5})& = & 5x+\frac{4}{9} \\\Leftrightarrow & 18x+\frac{18}{5}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{810}{ \color{blue}{45} }x+ \frac{162}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 810x \color{red}{+162} & = & \color{red}{225x} +20 \\\Leftrightarrow & 810x \color{red}{+162} \color{blue}{-162} \color{blue}{-225x} & = & \color{red}{225x} +20 \color{blue}{-225x} \color{blue}{-162} \\\Leftrightarrow & 810x-225x& = & 20-162 \\\Leftrightarrow & \color{red}{585} x& = & -142 \\\Leftrightarrow & x = \frac{-142}{585} & & \\ & V = \left\{ \frac{-142}{585} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{5}{12})& = & 7x+\frac{3}{10} \\\Leftrightarrow & -20x+\frac{25}{12}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 12 en 10 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-1200}{ \color{blue}{60} }x+ \frac{125}{ \color{blue}{60} })& = & (\frac{420}{ \color{blue}{60} }x+ \frac{18}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -1200x \color{red}{+125} & = & \color{red}{420x} +18 \\\Leftrightarrow & -1200x \color{red}{+125} \color{blue}{-125} \color{blue}{-420x} & = & \color{red}{420x} +18 \color{blue}{-420x} \color{blue}{-125} \\\Leftrightarrow & -1200x-420x& = & 18-125 \\\Leftrightarrow & \color{red}{-1620} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{-1620} & & \\\Leftrightarrow & x = \frac{107}{1620} & & \\ & V = \left\{ \frac{107}{1620} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{4}{7})& = & -7x+\frac{8}{9} \\\Leftrightarrow & 16x-\frac{16}{7}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1008}{ \color{blue}{63} }x- \frac{144}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1008x \color{red}{-144} & = & \color{red}{-441x} +56 \\\Leftrightarrow & 1008x \color{red}{-144} \color{blue}{+144} \color{blue}{+441x} & = & \color{red}{-441x} +56 \color{blue}{+441x} \color{blue}{+144} \\\Leftrightarrow & 1008x+441x& = & 56+144 \\\Leftrightarrow & \color{red}{1449} x& = & 200 \\\Leftrightarrow & x = \frac{200}{1449} & & \\ & V = \left\{ \frac{200}{1449} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{2})& = & -9x+\frac{10}{3} \\\Leftrightarrow & 10x-\frac{25}{2}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{60}{ \color{blue}{6} }x- \frac{75}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 60x \color{red}{-75} & = & \color{red}{-54x} +20 \\\Leftrightarrow & 60x \color{red}{-75} \color{blue}{+75} \color{blue}{+54x} & = & \color{red}{-54x} +20 \color{blue}{+54x} \color{blue}{+75} \\\Leftrightarrow & 60x+54x& = & 20+75 \\\Leftrightarrow & \color{red}{114} x& = & 95 \\\Leftrightarrow & x = \frac{95}{114} & & \\\Leftrightarrow & x = \frac{5}{6} & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{5}{4})& = & -3x+\frac{9}{2} \\\Leftrightarrow & 10x-\frac{25}{4}& = & -3x+\frac{9}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{40}{ \color{blue}{4} }x- \frac{25}{ \color{blue}{4} })& = & (\frac{-12}{ \color{blue}{4} }x+ \frac{18}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 40x \color{red}{-25} & = & \color{red}{-12x} +18 \\\Leftrightarrow & 40x \color{red}{-25} \color{blue}{+25} \color{blue}{+12x} & = & \color{red}{-12x} +18 \color{blue}{+12x} \color{blue}{+25} \\\Leftrightarrow & 40x+12x& = & 18+25 \\\Leftrightarrow & \color{red}{52} x& = & 43 \\\Leftrightarrow & x = \frac{43}{52} & & \\ & V = \left\{ \frac{43}{52} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{3}{7})& = & -3x+\frac{7}{4} \\\Leftrightarrow & 8x-\frac{6}{7}& = & -3x+\frac{7}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{224}{ \color{blue}{28} }x- \frac{24}{ \color{blue}{28} })& = & (\frac{-84}{ \color{blue}{28} }x+ \frac{49}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 224x \color{red}{-24} & = & \color{red}{-84x} +49 \\\Leftrightarrow & 224x \color{red}{-24} \color{blue}{+24} \color{blue}{+84x} & = & \color{red}{-84x} +49 \color{blue}{+84x} \color{blue}{+24} \\\Leftrightarrow & 224x+84x& = & 49+24 \\\Leftrightarrow & \color{red}{308} x& = & 73 \\\Leftrightarrow & x = \frac{73}{308} & & \\ & V = \left\{ \frac{73}{308} \right\} & \\\end{align}\)