Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-1)& = & 3x+\frac{4}{3} \\\Leftrightarrow & 10x+5& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 1 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{30}{ \color{blue}{3} }x+ \frac{15}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 30x \color{red}{+15} & = & \color{red}{9x} +4 \\\Leftrightarrow & 30x \color{red}{+15} \color{blue}{-15} \color{blue}{-9x} & = & \color{red}{9x} +4 \color{blue}{-9x} \color{blue}{-15} \\\Leftrightarrow & 30x-9x& = & 4-15 \\\Leftrightarrow & \color{red}{21} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{21} & & \\ & V = \left\{ \frac{-11}{21} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{2}{11})& = & 5x+\frac{2}{11} \\\Leftrightarrow & 12x-\frac{8}{11}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{132}{ \color{blue}{11} }x- \frac{8}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 132x \color{red}{-8} & = & \color{red}{55x} +2 \\\Leftrightarrow & 132x \color{red}{-8} \color{blue}{+8} \color{blue}{-55x} & = & \color{red}{55x} +2 \color{blue}{-55x} \color{blue}{+8} \\\Leftrightarrow & 132x-55x& = & 2+8 \\\Leftrightarrow & \color{red}{77} x& = & 10 \\\Leftrightarrow & x = \frac{10}{77} & & \\ & V = \left\{ \frac{10}{77} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{2}{5})& = & -5x+\frac{4}{7} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-84} & = & \color{red}{-175x} +20 \\\Leftrightarrow & -420x \color{red}{-84} \color{blue}{+84} \color{blue}{+175x} & = & \color{red}{-175x} +20 \color{blue}{+175x} \color{blue}{+84} \\\Leftrightarrow & -420x+175x& = & 20+84 \\\Leftrightarrow & \color{red}{-245} x& = & 104 \\\Leftrightarrow & x = \frac{104}{-245} & & \\\Leftrightarrow & x = \frac{-104}{245} & & \\ & V = \left\{ \frac{-104}{245} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{3}{5})& = & -5x+\frac{7}{2} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{-24} & = & \color{red}{-50x} +35 \\\Leftrightarrow & 120x \color{red}{-24} \color{blue}{+24} \color{blue}{+50x} & = & \color{red}{-50x} +35 \color{blue}{+50x} \color{blue}{+24} \\\Leftrightarrow & 120x+50x& = & 35+24 \\\Leftrightarrow & \color{red}{170} x& = & 59 \\\Leftrightarrow & x = \frac{59}{170} & & \\ & V = \left\{ \frac{59}{170} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{4}{11})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -12x-\frac{12}{11}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-84} & = & \color{red}{385x} +110 \\\Leftrightarrow & -924x \color{red}{-84} \color{blue}{+84} \color{blue}{-385x} & = & \color{red}{385x} +110 \color{blue}{-385x} \color{blue}{+84} \\\Leftrightarrow & -924x-385x& = & 110+84 \\\Leftrightarrow & \color{red}{-1309} x& = & 194 \\\Leftrightarrow & x = \frac{194}{-1309} & & \\\Leftrightarrow & x = \frac{-194}{1309} & & \\ & V = \left\{ \frac{-194}{1309} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{2}{5})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -24x+\frac{12}{5}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-360}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -360x \color{red}{+36} & = & \color{red}{75x} +10 \\\Leftrightarrow & -360x \color{red}{+36} \color{blue}{-36} \color{blue}{-75x} & = & \color{red}{75x} +10 \color{blue}{-75x} \color{blue}{-36} \\\Leftrightarrow & -360x-75x& = & 10-36 \\\Leftrightarrow & \color{red}{-435} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-435} & & \\\Leftrightarrow & x = \frac{26}{435} & & \\ & V = \left\{ \frac{26}{435} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{2}{5})& = & 5x+\frac{4}{7} \\\Leftrightarrow & 6x+\frac{6}{5}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{+42} & = & \color{red}{175x} +20 \\\Leftrightarrow & 210x \color{red}{+42} \color{blue}{-42} \color{blue}{-175x} & = & \color{red}{175x} +20 \color{blue}{-175x} \color{blue}{-42} \\\Leftrightarrow & 210x-175x& = & 20-42 \\\Leftrightarrow & \color{red}{35} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{35} & & \\ & V = \left\{ \frac{-22}{35} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{5}{8})& = & 7x+\frac{7}{2} \\\Leftrightarrow & 20x+\frac{25}{8}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{160}{ \color{blue}{8} }x+ \frac{25}{ \color{blue}{8} })& = & (\frac{56}{ \color{blue}{8} }x+ \frac{28}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 160x \color{red}{+25} & = & \color{red}{56x} +28 \\\Leftrightarrow & 160x \color{red}{+25} \color{blue}{-25} \color{blue}{-56x} & = & \color{red}{56x} +28 \color{blue}{-56x} \color{blue}{-25} \\\Leftrightarrow & 160x-56x& = & 28-25 \\\Leftrightarrow & \color{red}{104} x& = & 3 \\\Leftrightarrow & x = \frac{3}{104} & & \\ & V = \left\{ \frac{3}{104} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{4}{5})& = & 6x+\frac{10}{11} \\\Leftrightarrow & -18x-\frac{24}{5}& = & 6x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x- \frac{264}{ \color{blue}{55} })& = & (\frac{330}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{-264} & = & \color{red}{330x} +50 \\\Leftrightarrow & -990x \color{red}{-264} \color{blue}{+264} \color{blue}{-330x} & = & \color{red}{330x} +50 \color{blue}{-330x} \color{blue}{+264} \\\Leftrightarrow & -990x-330x& = & 50+264 \\\Leftrightarrow & \color{red}{-1320} x& = & 314 \\\Leftrightarrow & x = \frac{314}{-1320} & & \\\Leftrightarrow & x = \frac{-157}{660} & & \\ & V = \left\{ \frac{-157}{660} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{2}{3})& = & 5x+\frac{5}{8} \\\Leftrightarrow & -4x-\frac{4}{3}& = & 5x+\frac{5}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-96}{ \color{blue}{24} }x- \frac{32}{ \color{blue}{24} })& = & (\frac{120}{ \color{blue}{24} }x+ \frac{15}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -96x \color{red}{-32} & = & \color{red}{120x} +15 \\\Leftrightarrow & -96x \color{red}{-32} \color{blue}{+32} \color{blue}{-120x} & = & \color{red}{120x} +15 \color{blue}{-120x} \color{blue}{+32} \\\Leftrightarrow & -96x-120x& = & 15+32 \\\Leftrightarrow & \color{red}{-216} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-216} & & \\\Leftrightarrow & x = \frac{-47}{216} & & \\ & V = \left\{ \frac{-47}{216} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{4}{11})& = & -3x+\frac{7}{6} \\\Leftrightarrow & 14x+\frac{28}{11}& = & -3x+\frac{7}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{924}{ \color{blue}{66} }x+ \frac{168}{ \color{blue}{66} })& = & (\frac{-198}{ \color{blue}{66} }x+ \frac{77}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 924x \color{red}{+168} & = & \color{red}{-198x} +77 \\\Leftrightarrow & 924x \color{red}{+168} \color{blue}{-168} \color{blue}{+198x} & = & \color{red}{-198x} +77 \color{blue}{+198x} \color{blue}{-168} \\\Leftrightarrow & 924x+198x& = & 77-168 \\\Leftrightarrow & \color{red}{1122} x& = & -91 \\\Leftrightarrow & x = \frac{-91}{1122} & & \\ & V = \left\{ \frac{-91}{1122} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{3}{11})& = & -7x+\frac{8}{7} \\\Leftrightarrow & 6x+\frac{6}{11}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{+42} & = & \color{red}{-539x} +88 \\\Leftrightarrow & 462x \color{red}{+42} \color{blue}{-42} \color{blue}{+539x} & = & \color{red}{-539x} +88 \color{blue}{+539x} \color{blue}{-42} \\\Leftrightarrow & 462x+539x& = & 88-42 \\\Leftrightarrow & \color{red}{1001} x& = & 46 \\\Leftrightarrow & x = \frac{46}{1001} & & \\ & V = \left\{ \frac{46}{1001} \right\} & \\\end{align}\)