Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{5}{7})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{15}{7}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{75}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-75} & = & \color{red}{175x} +42 \\\Leftrightarrow & 420x \color{red}{-75} \color{blue}{+75} \color{blue}{-175x} & = & \color{red}{175x} +42 \color{blue}{-175x} \color{blue}{+75} \\\Leftrightarrow & 420x-175x& = & 42+75 \\\Leftrightarrow & \color{red}{245} x& = & 117 \\\Leftrightarrow & x = \frac{117}{245} & & \\ & V = \left\{ \frac{117}{245} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{5}{11})& = & -3x+\frac{2}{3} \\\Leftrightarrow & 10x+\frac{10}{11}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{330}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 330x \color{red}{+30} & = & \color{red}{-99x} +22 \\\Leftrightarrow & 330x \color{red}{+30} \color{blue}{-30} \color{blue}{+99x} & = & \color{red}{-99x} +22 \color{blue}{+99x} \color{blue}{-30} \\\Leftrightarrow & 330x+99x& = & 22-30 \\\Leftrightarrow & \color{red}{429} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{429} & & \\ & V = \left\{ \frac{-8}{429} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{5}{11})& = & -7x+\frac{2}{5} \\\Leftrightarrow & -16x-\frac{20}{11}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-880}{ \color{blue}{55} }x- \frac{100}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -880x \color{red}{-100} & = & \color{red}{-385x} +22 \\\Leftrightarrow & -880x \color{red}{-100} \color{blue}{+100} \color{blue}{+385x} & = & \color{red}{-385x} +22 \color{blue}{+385x} \color{blue}{+100} \\\Leftrightarrow & -880x+385x& = & 22+100 \\\Leftrightarrow & \color{red}{-495} x& = & 122 \\\Leftrightarrow & x = \frac{122}{-495} & & \\\Leftrightarrow & x = \frac{-122}{495} & & \\ & V = \left\{ \frac{-122}{495} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{2}{3})& = & -4x+\frac{4}{9} \\\Leftrightarrow & 21x+\frac{14}{3}& = & -4x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{189}{ \color{blue}{9} }x+ \frac{42}{ \color{blue}{9} })& = & (\frac{-36}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 189x \color{red}{+42} & = & \color{red}{-36x} +4 \\\Leftrightarrow & 189x \color{red}{+42} \color{blue}{-42} \color{blue}{+36x} & = & \color{red}{-36x} +4 \color{blue}{+36x} \color{blue}{-42} \\\Leftrightarrow & 189x+36x& = & 4-42 \\\Leftrightarrow & \color{red}{225} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{225} & & \\ & V = \left\{ \frac{-38}{225} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{5}{2})& = & 6x+\frac{4}{3} \\\Leftrightarrow & -35x+\frac{35}{2}& = & 6x+\frac{4}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-210}{ \color{blue}{6} }x+ \frac{105}{ \color{blue}{6} })& = & (\frac{36}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -210x \color{red}{+105} & = & \color{red}{36x} +8 \\\Leftrightarrow & -210x \color{red}{+105} \color{blue}{-105} \color{blue}{-36x} & = & \color{red}{36x} +8 \color{blue}{-36x} \color{blue}{-105} \\\Leftrightarrow & -210x-36x& = & 8-105 \\\Leftrightarrow & \color{red}{-246} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{-246} & & \\\Leftrightarrow & x = \frac{97}{246} & & \\ & V = \left\{ \frac{97}{246} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{4}{3})& = & 8x+\frac{7}{2} \\\Leftrightarrow & -21x+\frac{28}{3}& = & 8x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-126}{ \color{blue}{6} }x+ \frac{56}{ \color{blue}{6} })& = & (\frac{48}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -126x \color{red}{+56} & = & \color{red}{48x} +21 \\\Leftrightarrow & -126x \color{red}{+56} \color{blue}{-56} \color{blue}{-48x} & = & \color{red}{48x} +21 \color{blue}{-48x} \color{blue}{-56} \\\Leftrightarrow & -126x-48x& = & 21-56 \\\Leftrightarrow & \color{red}{-174} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{-174} & & \\\Leftrightarrow & x = \frac{35}{174} & & \\ & V = \left\{ \frac{35}{174} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{2}{5})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -9x+\frac{6}{5}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{+42} & = & \color{red}{-175x} +10 \\\Leftrightarrow & -315x \color{red}{+42} \color{blue}{-42} \color{blue}{+175x} & = & \color{red}{-175x} +10 \color{blue}{+175x} \color{blue}{-42} \\\Leftrightarrow & -315x+175x& = & 10-42 \\\Leftrightarrow & \color{red}{-140} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{-140} & & \\\Leftrightarrow & x = \frac{8}{35} & & \\ & V = \left\{ \frac{8}{35} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{3}{7})& = & 7x+\frac{9}{10} \\\Leftrightarrow & -6x-\frac{9}{7}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-420}{ \color{blue}{70} }x- \frac{90}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -420x \color{red}{-90} & = & \color{red}{490x} +63 \\\Leftrightarrow & -420x \color{red}{-90} \color{blue}{+90} \color{blue}{-490x} & = & \color{red}{490x} +63 \color{blue}{-490x} \color{blue}{+90} \\\Leftrightarrow & -420x-490x& = & 63+90 \\\Leftrightarrow & \color{red}{-910} x& = & 153 \\\Leftrightarrow & x = \frac{153}{-910} & & \\\Leftrightarrow & x = \frac{-153}{910} & & \\ & V = \left\{ \frac{-153}{910} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{5}{7})& = & -3x+\frac{7}{3} \\\Leftrightarrow & 16x+\frac{20}{7}& = & -3x+\frac{7}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{49}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{+60} & = & \color{red}{-63x} +49 \\\Leftrightarrow & 336x \color{red}{+60} \color{blue}{-60} \color{blue}{+63x} & = & \color{red}{-63x} +49 \color{blue}{+63x} \color{blue}{-60} \\\Leftrightarrow & 336x+63x& = & 49-60 \\\Leftrightarrow & \color{red}{399} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{399} & & \\ & V = \left\{ \frac{-11}{399} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{4}{7})& = & 5x+\frac{4}{9} \\\Leftrightarrow & -14x+4& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 1 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-126}{ \color{blue}{9} }x+ \frac{36}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -126x \color{red}{+36} & = & \color{red}{45x} +4 \\\Leftrightarrow & -126x \color{red}{+36} \color{blue}{-36} \color{blue}{-45x} & = & \color{red}{45x} +4 \color{blue}{-45x} \color{blue}{-36} \\\Leftrightarrow & -126x-45x& = & 4-36 \\\Leftrightarrow & \color{red}{-171} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{-171} & & \\\Leftrightarrow & x = \frac{32}{171} & & \\ & V = \left\{ \frac{32}{171} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{3}{11})& = & 5x+\frac{7}{6} \\\Leftrightarrow & 6x+\frac{6}{11}& = & 5x+\frac{7}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{396}{ \color{blue}{66} }x+ \frac{36}{ \color{blue}{66} })& = & (\frac{330}{ \color{blue}{66} }x+ \frac{77}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 396x \color{red}{+36} & = & \color{red}{330x} +77 \\\Leftrightarrow & 396x \color{red}{+36} \color{blue}{-36} \color{blue}{-330x} & = & \color{red}{330x} +77 \color{blue}{-330x} \color{blue}{-36} \\\Leftrightarrow & 396x-330x& = & 77-36 \\\Leftrightarrow & \color{red}{66} x& = & 41 \\\Leftrightarrow & x = \frac{41}{66} & & \\ & V = \left\{ \frac{41}{66} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{5}{7})& = & -9x+\frac{3}{4} \\\Leftrightarrow & -18x-\frac{30}{7}& = & -9x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-504}{ \color{blue}{28} }x- \frac{120}{ \color{blue}{28} })& = & (\frac{-252}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -504x \color{red}{-120} & = & \color{red}{-252x} +21 \\\Leftrightarrow & -504x \color{red}{-120} \color{blue}{+120} \color{blue}{+252x} & = & \color{red}{-252x} +21 \color{blue}{+252x} \color{blue}{+120} \\\Leftrightarrow & -504x+252x& = & 21+120 \\\Leftrightarrow & \color{red}{-252} x& = & 141 \\\Leftrightarrow & x = \frac{141}{-252} & & \\\Leftrightarrow & x = \frac{-47}{84} & & \\ & V = \left\{ \frac{-47}{84} \right\} & \\\end{align}\)