Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{2}{7})& = & -7x+\frac{8}{7} \\\Leftrightarrow & -9x-\frac{6}{7}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-63}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -63x \color{red}{-6} & = & \color{red}{-49x} +8 \\\Leftrightarrow & -63x \color{red}{-6} \color{blue}{+6} \color{blue}{+49x} & = & \color{red}{-49x} +8 \color{blue}{+49x} \color{blue}{+6} \\\Leftrightarrow & -63x+49x& = & 8+6 \\\Leftrightarrow & \color{red}{-14} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-14} & & \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{3}{8})& = & 4x+\frac{10}{3} \\\Leftrightarrow & -35x-\frac{21}{8}& = & 4x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-840}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{96}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -840x \color{red}{-63} & = & \color{red}{96x} +80 \\\Leftrightarrow & -840x \color{red}{-63} \color{blue}{+63} \color{blue}{-96x} & = & \color{red}{96x} +80 \color{blue}{-96x} \color{blue}{+63} \\\Leftrightarrow & -840x-96x& = & 80+63 \\\Leftrightarrow & \color{red}{-936} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-936} & & \\\Leftrightarrow & x = \frac{-11}{72} & & \\ & V = \left\{ \frac{-11}{72} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{5}{7})& = & -9x+\frac{5}{2} \\\Leftrightarrow & -8x+\frac{10}{7}& = & -9x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-112}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} })& = & (\frac{-126}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -112x \color{red}{+20} & = & \color{red}{-126x} +35 \\\Leftrightarrow & -112x \color{red}{+20} \color{blue}{-20} \color{blue}{+126x} & = & \color{red}{-126x} +35 \color{blue}{+126x} \color{blue}{-20} \\\Leftrightarrow & -112x+126x& = & 35-20 \\\Leftrightarrow & \color{red}{14} x& = & 15 \\\Leftrightarrow & x = \frac{15}{14} & & \\ & V = \left\{ \frac{15}{14} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{3}{5})& = & 9x+\frac{8}{3} \\\Leftrightarrow & -20x+\frac{12}{5}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{+36} & = & \color{red}{135x} +40 \\\Leftrightarrow & -300x \color{red}{+36} \color{blue}{-36} \color{blue}{-135x} & = & \color{red}{135x} +40 \color{blue}{-135x} \color{blue}{-36} \\\Leftrightarrow & -300x-135x& = & 40-36 \\\Leftrightarrow & \color{red}{-435} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-435} & & \\\Leftrightarrow & x = \frac{-4}{435} & & \\ & V = \left\{ \frac{-4}{435} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{4}{11})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -6x+\frac{12}{11}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-66}{ \color{blue}{11} }x+ \frac{12}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -66x \color{red}{+12} & = & \color{red}{77x} +6 \\\Leftrightarrow & -66x \color{red}{+12} \color{blue}{-12} \color{blue}{-77x} & = & \color{red}{77x} +6 \color{blue}{-77x} \color{blue}{-12} \\\Leftrightarrow & -66x-77x& = & 6-12 \\\Leftrightarrow & \color{red}{-143} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-143} & & \\\Leftrightarrow & x = \frac{6}{143} & & \\ & V = \left\{ \frac{6}{143} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{4}{11})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -6x+\frac{12}{11}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{84}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+84} & = & \color{red}{-539x} +110 \\\Leftrightarrow & -462x \color{red}{+84} \color{blue}{-84} \color{blue}{+539x} & = & \color{red}{-539x} +110 \color{blue}{+539x} \color{blue}{-84} \\\Leftrightarrow & -462x+539x& = & 110-84 \\\Leftrightarrow & \color{red}{77} x& = & 26 \\\Leftrightarrow & x = \frac{26}{77} & & \\ & V = \left\{ \frac{26}{77} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{5}{2})& = & -3x+\frac{5}{4} \\\Leftrightarrow & -20x-\frac{25}{2}& = & -3x+\frac{5}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-80}{ \color{blue}{4} }x- \frac{50}{ \color{blue}{4} })& = & (\frac{-12}{ \color{blue}{4} }x+ \frac{5}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -80x \color{red}{-50} & = & \color{red}{-12x} +5 \\\Leftrightarrow & -80x \color{red}{-50} \color{blue}{+50} \color{blue}{+12x} & = & \color{red}{-12x} +5 \color{blue}{+12x} \color{blue}{+50} \\\Leftrightarrow & -80x+12x& = & 5+50 \\\Leftrightarrow & \color{red}{-68} x& = & 55 \\\Leftrightarrow & x = \frac{55}{-68} & & \\\Leftrightarrow & x = \frac{-55}{68} & & \\ & V = \left\{ \frac{-55}{68} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{4}{5})& = & 7x+\frac{5}{7} \\\Leftrightarrow & -28x+\frac{28}{5}& = & 7x+\frac{5}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-980}{ \color{blue}{35} }x+ \frac{196}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{25}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -980x \color{red}{+196} & = & \color{red}{245x} +25 \\\Leftrightarrow & -980x \color{red}{+196} \color{blue}{-196} \color{blue}{-245x} & = & \color{red}{245x} +25 \color{blue}{-245x} \color{blue}{-196} \\\Leftrightarrow & -980x-245x& = & 25-196 \\\Leftrightarrow & \color{red}{-1225} x& = & -171 \\\Leftrightarrow & x = \frac{-171}{-1225} & & \\\Leftrightarrow & x = \frac{171}{1225} & & \\ & V = \left\{ \frac{171}{1225} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{3}{8})& = & -4x+\frac{4}{3} \\\Leftrightarrow & -15x-\frac{15}{8}& = & -4x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-360}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{-96}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -360x \color{red}{-45} & = & \color{red}{-96x} +32 \\\Leftrightarrow & -360x \color{red}{-45} \color{blue}{+45} \color{blue}{+96x} & = & \color{red}{-96x} +32 \color{blue}{+96x} \color{blue}{+45} \\\Leftrightarrow & -360x+96x& = & 32+45 \\\Leftrightarrow & \color{red}{-264} x& = & 77 \\\Leftrightarrow & x = \frac{77}{-264} & & \\\Leftrightarrow & x = \frac{-7}{24} & & \\ & V = \left\{ \frac{-7}{24} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{4}{7})& = & 5x+\frac{10}{11} \\\Leftrightarrow & -12x+\frac{24}{7}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{264}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+264} & = & \color{red}{385x} +70 \\\Leftrightarrow & -924x \color{red}{+264} \color{blue}{-264} \color{blue}{-385x} & = & \color{red}{385x} +70 \color{blue}{-385x} \color{blue}{-264} \\\Leftrightarrow & -924x-385x& = & 70-264 \\\Leftrightarrow & \color{red}{-1309} x& = & -194 \\\Leftrightarrow & x = \frac{-194}{-1309} & & \\\Leftrightarrow & x = \frac{194}{1309} & & \\ & V = \left\{ \frac{194}{1309} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{4}{11})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -20x+\frac{16}{11}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x+ \frac{48}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{+48} & = & \color{red}{231x} +88 \\\Leftrightarrow & -660x \color{red}{+48} \color{blue}{-48} \color{blue}{-231x} & = & \color{red}{231x} +88 \color{blue}{-231x} \color{blue}{-48} \\\Leftrightarrow & -660x-231x& = & 88-48 \\\Leftrightarrow & \color{red}{-891} x& = & 40 \\\Leftrightarrow & x = \frac{40}{-891} & & \\\Leftrightarrow & x = \frac{-40}{891} & & \\ & V = \left\{ \frac{-40}{891} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{3}{11})& = & 5x+\frac{5}{9} \\\Leftrightarrow & 18x+\frac{18}{11}& = & 5x+\frac{5}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1782}{ \color{blue}{99} }x+ \frac{162}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{55}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1782x \color{red}{+162} & = & \color{red}{495x} +55 \\\Leftrightarrow & 1782x \color{red}{+162} \color{blue}{-162} \color{blue}{-495x} & = & \color{red}{495x} +55 \color{blue}{-495x} \color{blue}{-162} \\\Leftrightarrow & 1782x-495x& = & 55-162 \\\Leftrightarrow & \color{red}{1287} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{1287} & & \\ & V = \left\{ \frac{-107}{1287} \right\} & \\\end{align}\)