Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{5}{2})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -6x+\frac{15}{2}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-36}{ \color{blue}{6} }x+ \frac{45}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -36x \color{red}{+45} & = & \color{red}{-42x} +16 \\\Leftrightarrow & -36x \color{red}{+45} \color{blue}{-45} \color{blue}{+42x} & = & \color{red}{-42x} +16 \color{blue}{+42x} \color{blue}{-45} \\\Leftrightarrow & -36x+42x& = & 16-45 \\\Leftrightarrow & \color{red}{6} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{6} & & \\ & V = \left\{ \frac{-29}{6} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{5}{7})& = & 3x+\frac{10}{3} \\\Leftrightarrow & -8x-\frac{20}{7}& = & 3x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{-60} & = & \color{red}{63x} +70 \\\Leftrightarrow & -168x \color{red}{-60} \color{blue}{+60} \color{blue}{-63x} & = & \color{red}{63x} +70 \color{blue}{-63x} \color{blue}{+60} \\\Leftrightarrow & -168x-63x& = & 70+60 \\\Leftrightarrow & \color{red}{-231} x& = & 130 \\\Leftrightarrow & x = \frac{130}{-231} & & \\\Leftrightarrow & x = \frac{-130}{231} & & \\ & V = \left\{ \frac{-130}{231} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{3})& = & -7x+\frac{2}{5} \\\Leftrightarrow & -6x+\frac{10}{3}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{+50} & = & \color{red}{-105x} +6 \\\Leftrightarrow & -90x \color{red}{+50} \color{blue}{-50} \color{blue}{+105x} & = & \color{red}{-105x} +6 \color{blue}{+105x} \color{blue}{-50} \\\Leftrightarrow & -90x+105x& = & 6-50 \\\Leftrightarrow & \color{red}{15} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{15} & & \\ & V = \left\{ \frac{-44}{15} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{4}{5})& = & -2x+\frac{7}{11} \\\Leftrightarrow & 15x+\frac{12}{5}& = & -2x+\frac{7}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-110}{ \color{blue}{55} }x+ \frac{35}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{+132} & = & \color{red}{-110x} +35 \\\Leftrightarrow & 825x \color{red}{+132} \color{blue}{-132} \color{blue}{+110x} & = & \color{red}{-110x} +35 \color{blue}{+110x} \color{blue}{-132} \\\Leftrightarrow & 825x+110x& = & 35-132 \\\Leftrightarrow & \color{red}{935} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{935} & & \\ & V = \left\{ \frac{-97}{935} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{1}{2})& = & -3x+\frac{9}{4} \\\Leftrightarrow & 25x+\frac{5}{2}& = & -3x+\frac{9}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{100}{ \color{blue}{4} }x+ \frac{10}{ \color{blue}{4} })& = & (\frac{-12}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 100x \color{red}{+10} & = & \color{red}{-12x} +9 \\\Leftrightarrow & 100x \color{red}{+10} \color{blue}{-10} \color{blue}{+12x} & = & \color{red}{-12x} +9 \color{blue}{+12x} \color{blue}{-10} \\\Leftrightarrow & 100x+12x& = & 9-10 \\\Leftrightarrow & \color{red}{112} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{112} & & \\ & V = \left\{ \frac{-1}{112} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{3}{11})& = & -3x+\frac{9}{11} \\\Leftrightarrow & -18x-\frac{18}{11}& = & -3x+\frac{9}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-198}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{9}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -198x \color{red}{-18} & = & \color{red}{-33x} +9 \\\Leftrightarrow & -198x \color{red}{-18} \color{blue}{+18} \color{blue}{+33x} & = & \color{red}{-33x} +9 \color{blue}{+33x} \color{blue}{+18} \\\Leftrightarrow & -198x+33x& = & 9+18 \\\Leftrightarrow & \color{red}{-165} x& = & 27 \\\Leftrightarrow & x = \frac{27}{-165} & & \\\Leftrightarrow & x = \frac{-9}{55} & & \\ & V = \left\{ \frac{-9}{55} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{4}{7})& = & 5x+\frac{7}{11} \\\Leftrightarrow & -12x-\frac{24}{7}& = & 5x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{264}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-264} & = & \color{red}{385x} +49 \\\Leftrightarrow & -924x \color{red}{-264} \color{blue}{+264} \color{blue}{-385x} & = & \color{red}{385x} +49 \color{blue}{-385x} \color{blue}{+264} \\\Leftrightarrow & -924x-385x& = & 49+264 \\\Leftrightarrow & \color{red}{-1309} x& = & 313 \\\Leftrightarrow & x = \frac{313}{-1309} & & \\\Leftrightarrow & x = \frac{-313}{1309} & & \\ & V = \left\{ \frac{-313}{1309} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{2}{7})& = & 7x+\frac{3}{4} \\\Leftrightarrow & 12x+\frac{6}{7}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{336}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 336x \color{red}{+24} & = & \color{red}{196x} +21 \\\Leftrightarrow & 336x \color{red}{+24} \color{blue}{-24} \color{blue}{-196x} & = & \color{red}{196x} +21 \color{blue}{-196x} \color{blue}{-24} \\\Leftrightarrow & 336x-196x& = & 21-24 \\\Leftrightarrow & \color{red}{140} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{140} & & \\ & V = \left\{ \frac{-3}{140} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{1}{2})& = & 4x+\frac{5}{6} \\\Leftrightarrow & 21x-\frac{7}{2}& = & 4x+\frac{5}{6} \\ & & & \text{kgv van noemers 2 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{126}{ \color{blue}{6} }x- \frac{21}{ \color{blue}{6} })& = & (\frac{24}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 126x \color{red}{-21} & = & \color{red}{24x} +5 \\\Leftrightarrow & 126x \color{red}{-21} \color{blue}{+21} \color{blue}{-24x} & = & \color{red}{24x} +5 \color{blue}{-24x} \color{blue}{+21} \\\Leftrightarrow & 126x-24x& = & 5+21 \\\Leftrightarrow & \color{red}{102} x& = & 26 \\\Leftrightarrow & x = \frac{26}{102} & & \\\Leftrightarrow & x = \frac{13}{51} & & \\ & V = \left\{ \frac{13}{51} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{2}{3})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 28x-\frac{14}{3}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{588}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 588x \color{red}{-98} & = & \color{red}{105x} +30 \\\Leftrightarrow & 588x \color{red}{-98} \color{blue}{+98} \color{blue}{-105x} & = & \color{red}{105x} +30 \color{blue}{-105x} \color{blue}{+98} \\\Leftrightarrow & 588x-105x& = & 30+98 \\\Leftrightarrow & \color{red}{483} x& = & 128 \\\Leftrightarrow & x = \frac{128}{483} & & \\ & V = \left\{ \frac{128}{483} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{4}{5})& = & 7x+\frac{4}{5} \\\Leftrightarrow & -6x+\frac{12}{5}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-30}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -30x \color{red}{+12} & = & \color{red}{35x} +4 \\\Leftrightarrow & -30x \color{red}{+12} \color{blue}{-12} \color{blue}{-35x} & = & \color{red}{35x} +4 \color{blue}{-35x} \color{blue}{-12} \\\Leftrightarrow & -30x-35x& = & 4-12 \\\Leftrightarrow & \color{red}{-65} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-65} & & \\\Leftrightarrow & x = \frac{8}{65} & & \\ & V = \left\{ \frac{8}{65} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{4}{5})& = & 5x+\frac{10}{11} \\\Leftrightarrow & -12x+\frac{16}{5}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{176}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+176} & = & \color{red}{275x} +50 \\\Leftrightarrow & -660x \color{red}{+176} \color{blue}{-176} \color{blue}{-275x} & = & \color{red}{275x} +50 \color{blue}{-275x} \color{blue}{-176} \\\Leftrightarrow & -660x-275x& = & 50-176 \\\Leftrightarrow & \color{red}{-935} x& = & -126 \\\Leftrightarrow & x = \frac{-126}{-935} & & \\\Leftrightarrow & x = \frac{126}{935} & & \\ & V = \left\{ \frac{126}{935} \right\} & \\\end{align}\)